Questions tagged [slope]
For questions on finding or applying slope, a number that describes both the direction and the steepness of a line.
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Can you find an equation parallel or perpendicular to a line when it is not in slope intercept form?
For example, if I need to find the equation of the line parallel to $$2x-3y=4$$ which passes through the point $(1,-5)$ I know how to do this by putting it into slope-intercept form first to find the ...
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1answer
36 views
Gradient of a velocity vector
Apologies if this is extremely simple. I'm a biology undergrad and I need this to measure cell membranes but I'm really struggling to find a solution anywhere.
I'm trying to find the gradient of a ...
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1answer
19 views
The prolate cycloid
A cycloid is given by the parametric equations:
$ x = 2 - \pi \cos(t)$ and $ y = 2t - \pi \sin(t)$.
The problem asks for the slope of the tangents on the cycloid at a point where the cycloid ...
2
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2answers
32 views
Calculating tangent line at $t=2$
Calculate the tangent line at $t=2$ of the curve
$$x(t)=t^2+2t+4,\ y(t)=1+te^t$$
How would you go about determining this? So far I have
$$x'(t)=2t + 2\\
y'(t) = te^t+e^t$$
Where do I go from here ...
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1answer
15 views
Decrease at an Increasing rate
I need a formula that decreases at an increasing rate. I'm guessing that logarithm is involved in the answer. My criteria:
A value of 20 must return a value of 20 (low bound)
A value of 80 must return ...
2
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1answer
17 views
Correct algorithm for finding regions of increasing / decreasing and the relationship to critical points.
Yet again, I find myself confused about something that seems basic: critical points and regions of increasing / decreasing.
Previously, I thought that to identify regions of increasing / decreasing, ...
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6answers
552 views
Why limits give us the exact value of the slope of the tangent line?
Limits tell us how functions behave at $x\to a$, not how they behave at $x = a$. However, in limits we plug $x = a$ as an approximation of $x\to a$, so: why the limits give us the exact value of slope ...
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2answers
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What is the relation of this line $y = ax +b$ with the points $(x_1, y_1), (x_2, y_2)$
I have a two points with coordinates $(x_1, y_1), (x_2, y_2)$
I am given a line
$y = ax +b$
where $a = \dfrac{y_2-y_1}{x_2-x_1}$, $b = \dfrac{y_1x_2 - y_2x_1}{x_2-x_1}$
I wish to know the ...
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0answers
19 views
Why the value of x2 is reducing?
The slope is given by $ \frac{y1-y2}{x1-x2}$
If the slope is given we can also calculate the value of x2.
slope= $ \frac{y1-y2}{x1-x2}$
x1-x2= $\frac{y1-y2}{slope}$
x2=x1-$ \frac{y1-y2}{slope}$
...
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1answer
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Why is the gradient of $f(x)= x$ the vector $(1,0,0)$?
Why is the gradient of $f(x)= x$ the vector $(1,0,0)$? This would mean that at every point on the straight line $y = x$, I should go horizontally to experience the maximum change in slope. I was ...
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1answer
17 views
Calculating the regression coefficient of a time-based series
If i have a sample (lets say house price in millions over time) where x=1,2,...,14 samples y-values are shown in the image below, with one sample estimated per month.
How do i calculate the estimated ...
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1answer
171 views
(Calculus) Derivative Thinking Question
Recently, my Calculus and Vectors (Grade 12) teacher gave our class a thinking question/assignment to work on over the march break, and after working on for some time, I've become stuck on it.
The ...
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4answers
34 views
The formula of Slope. [closed]
The equation of the slope is m= $\frac{\Delta Y} {\Delta X} $. But why not the other way around? Why not m= $\frac{\Delta X} {\Delta Y} $ ?
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2answers
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Finding the slope of a line, slightly confused by the answer
(just for context, this is from a study booklet for a military test. I haven't done algebra in about 10 years. I googled around but was having trouble finding specific information about the below.)
I ...
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3answers
48 views
How do I find ordered pair, given slope of the tangent line?
The function is $f(x) = x^3 + 9x^2 + 36x + 10$ and the slope given is $9$.
I found the derivative and set it equal to $9$, but I ended up with $x = (-9,-33)$ and the answer is $(-3,-44)$.
I've asked ...
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3answers
44 views
What is the slope of tangent line to a rotated ellipse at a specific point?
I've seen discussions about this but with too many details left out. I have an ellipse with the standard parameters: $h, k, a, b$ and a rotation angle. (I can convert all that to the general form ...
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3answers
125 views
Why $\infty×0=-1$ from multiplication of two slopes of two lines perpendicular to each other and how do we define infinity?
Here is given $A(x_1,y_1), B(x_1,y_2), C(x_2,y_3)$ and $D(x_3,y_3)$. I have recently read that, multiplication of two perpendicular lines is always $-1$.
From the above graph, the slope of $AB, m_1 = ...
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2answers
33 views
About the slope of a parametric curve at a point. (James Stewart Calculus 8th Edition.)
I am reading "Calculus 8th Edition" by James Stewart.
Suppose $f$ and $g$ are differentiable functions and we want to find the tangent line at a point on the parametric curve $x=f(t),y=g(t)$, ...
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4answers
50 views
find equation of tangent for function $f(x)$ parallel to a line [closed]
I dont have a clue how to solve this kind of problem.
I dont know how to find out slope of $\ln x$.
$f(x) = \ln x$
line $p: 2x-y-3=0$
I have searched for slope of $\ln x$, I know how find out ...
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1answer
48 views
What is the inclination (grade) of the trail?
In the problem:
A straight traail with a uniform inclination leads from a hotel, elevation $5000$ feet, to take a lake in a valley, elevation $600$ feet. The Length of the traill is $4100$ feet. What ...
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1answer
19 views
Why each component of gradient which is slope of the curve in itself while keeping other variables constant gives us slope of curve?
My doubt is suppose we assume a 3D space with 2D surface in it given by some function z = f(x,y). Then each component of the gradient is geometrically the slope of the tangent at f on either x-z or y-...
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1answer
30 views
Calculating error on slope of graph
I'm trying to find the rate of change and the error on that rate based on 7 measurements points and the assumption that the trend is linear. My calculations are below:
$$
\begin{array}{|c|c|c|c|}
\...
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2answers
28 views
Understanding calculating the intercept C between two points
I currently started with some basic geometry and I'm already stuck at some very very basic intuition regarding finding the line between two points in a plane.
I understand $y = mx + c$ and I am able ...
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votes
1answer
16 views
How to tell the run of a line segment where the area underneath it, starting point, and slope are known.
I have a program where I am currently solving for the difference of X₁ and X₂ of a line-segment where the area under the line-segment (A), the slope (s), and the starting point (X₁,Y₁) are known.
...
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3answers
33 views
Finding slope m of tangent to curve
been years since I took calculus and am currently struggling with how to properly work out the following:
Using the tanget line slope formula:
My understanding is that I would need to find the ...
2
votes
1answer
101 views
The slope of $nx\ \%\ m$
(There is a follow-up question at MO.)
Let $x\ \%\ m$ be the residue of $x$ modulo $m$, i.e.
$$x \equiv x\ \%\ m\pmod{m}$$
Let $\mu^n_m(x)$ denote multiplication by $n$ modulo $m$, i.e.
$$\mu^n_m(...
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2answers
36 views
Use Limits to calculate slope of the tangent
Use limits to calculate the slope of the tangent to the curve $y=\frac1x$ at $x=a$. I need to write an equation for the tangent to $y=\frac1x$ at $x=4$.
I think I understand the basics of the ...
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2answers
35 views
Finding the slope of the line normal to the graph at a given point
My Problem: What is the slope of the line normal to the graph of $f(x) = e^x-x^e-e$ at the point where the graph crosses the $x$-axis?
a. $-0.288$
b. $-0.110$
c. $3.471$
d. $9.106$
I ...
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3answers
53 views
Given only the slope, find the shortest distance from a line to a point on the x-axis
I have the following amusing question.
Suppose that the red dot is the point $x = -1$
The blue line is the line crossing the origin with slope $-1/k, k > 0$
I wish to find the length of the ...
3
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1answer
55 views
Quadratics: Intuitive relation between discriminant and derivative at roots
While working with quadratics that have real roots, I realized an interesting fact:
The slope of a quadratic at its roots is equal to $\pm \sqrt{D}$ where $D=b^2-4ac$
Proof:
$$f(x) = ax^2 + bx +c$$...
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2answers
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slope of a linear function in semi-log plot
I have a decreasing linear function. So,the slope of this function df/dt <0. Now, if we plot this function in a semi-log plot with log(t) in horizontal axis and y in vertical axis, can we say that ...
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2answers
102 views
How can I find the slope of a line tangent to a small circle on a sphere? [closed]
I draw a circle on the earth, so that it passes through the north pole. I then begin walking around the circle, keeping track of my latitude. How do I tell what direction that I'm facing by knowing ...
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1answer
36 views
how to find slope of discrete point?
I am wondering if it is possible to find the slope at each point in the following dataset,
...
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0answers
40 views
Sketch the slope field
I need to sketch the slope field for this ODE $ y'=\frac{y+x-6xe^{\frac{y}{x}-2}}{x} $.
The first step is $f(x,y)=\frac{y+x-6xe^{\frac{y}{x}-2}}{x}=c $, where $c=const$. Now I have to draw the curves ...
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1answer
38 views
How to shorten a line but maintain its angle? [closed]
I have a line that looks like this:
to draw this line i have the following:
point A: (x,y)
point B: (x,y)
so for example, i will be given this path:
(90,20),(400,300)
and then i can draw a line ...
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2answers
46 views
What is the unit of this “Rate of Change”?
This is the plot of the function $f(x) = 0.9x$.
So, the rate of change of $y$ with respect to $x$ is $0.9$.
My question is, what is the unit of this Rate of Change?
$0.9$ per $x$?
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1answer
22 views
calculate angle of line with negative slope
I want to use the formula
$$
tan(\alpha)=m
$$
for negative slopes but always get negative degrees. For instance, say the slope of a line $g$ is $-1$. Using the formula above (arctan$(-1)=\alpha$), I ...
2
votes
1answer
80 views
Does an endpoint of a function have a slope?
Say I have the following function which is defined for $0 \leq x \leq 1$:
If you would derive this function and substitute $y = 0$, you would get $x = 0.5$ and $x = 0.75$ for the respective as the ...
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0answers
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Find the value of Δx for which the value of Δy/Δx is within 0.1 units of slope.
Here is the link for the problem that I am trying to solve:
https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/1.-differentiation/part-a-definition-and-basic-rules/...
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0answers
35 views
When the slope of the angle bisector is 1, is the product of the slopes of the 2 lines forming the angle equal to 1
When the slope of the angle bisector is 1, I have been told that the product of the slopes of the 2 lines forming the original angle is 1. Is this true?
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1answer
24 views
Slope of a triangle where the sum of the height at each integer equals 1.
I have a problem where I'm trying to determine a proof to get the slope of a triangle $m$ in terms of $n$ where $\sum_{i=1}^n h_i = 1$.
I think I stumbled apon the answer being $m = \frac{2}{n(n+1)}$ ...
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0answers
31 views
Slope Intercept Form of a line - Derivation
Question: 1
I have 2 coordinates i.e. $(0,c)$ and $(x,y)$
Assumption y is less than c.
Find slope $(c-y) / (0-x) = m $
Simplify to get $y = mx + c$.
But the slope of the line connecting $(0, ...
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1answer
17 views
Determine the slope of a plane whose rise in z is zero, but whose change in x and y are not.
Determine the slope of a plane whose rise in z is zero, but whose change in x and y are not. Explain what this plane looks like.
Would it be a plane in the xy plane? Not sure how to start this ...
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2answers
25 views
How can I prove if l1 is as twice as steep as l2?
How do I find the slope of each line using SohCahToa? I plan on using the unit circle but I am having difficulty calculating slope.
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1answer
48 views
Would parallel lines in 2 parallel planes have the same slope?
If I am given 2 points in Plane A and 2 points in Plane B and I connected those points, would the lines have the same slopes? How can I show that algebraically?
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1answer
32 views
Kink versus jump
Suppose I have a function defined as follows
$n(r) = \begin{cases} n_h \quad \text{if} \quad r< \hat{r} \\ n_l \quad \text{if} \quad r \ge \hat{r}\end{cases}$. Where $n_h > n_l$ and $r \in [0,\...
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0answers
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Given a plane with mx = 1 and my = 2, find the slope in the direction when x both increases by 2 and y increases by 3. [closed]
Slope =rise/run would it be as simple as 6/2=3?
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0answers
25 views
Formula for finding the slope of a regression line
I want to calculate the gradient of a regression line and have been looking at various websites and books to find the formula for it. My school textbook writes that this is:
$$m={S_{xy}\over(S_x)^2}$$...
0
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1answer
54 views
Why is the slope of a linear equation of the form $ Ax + By + C = 0 $, $ - \frac {A}{B} $?
The slope of a linear equation of the form $ Ax + By + C = 0 $ (general form) is given by $- \frac {A}{B} $. Could someone intuitively explain why we use this formula?
I've read that this is ...
0
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0answers
18 views
vertically −a/b units for every 1 unit of movement horizontally as it is to say that linear equations move vertically −a units…
So I have previously asked a question and the user was very much helpful. But I am still having difficulty with the problem. This is what I have done so far. Can someone please guide me in the right ...
