Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [slope]

For questions on finding or applying slope, a number that describes both the direction and the steepness of a line.

4
votes
1answer
117 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 ...
0
votes
4answers
32 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} $ ?
2
votes
2answers
38 views

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 ...
1
vote
3answers
44 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 ...
0
votes
3answers
42 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 ...
1
vote
2answers
80 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 = ...
0
votes
2answers
31 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 $x=f(t),y=g(t)$, ...
1
vote
4answers
46 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 ...
0
votes
1answer
41 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 ...
0
votes
1answer
18 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-...
0
votes
1answer
24 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|} \...
0
votes
2answers
27 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 ...
0
votes
1answer
15 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. ...
2
votes
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
100 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(...
0
votes
2answers
27 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 ...
0
votes
2answers
25 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 ...
0
votes
3answers
45 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
votes
1answer
54 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: $$f(x) = ax^2 + bx +c$$...
1
vote
2answers
28 views

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 ...
0
votes
2answers
93 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 ...
0
votes
1answer
27 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, ...
1
vote
0answers
38 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 ...
-1
votes
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 ...
0
votes
2answers
45 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 $x$?
0
votes
1answer
20 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
45 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 ...
0
votes
0answers
86 views

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/...
0
votes
0answers
31 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?
0
votes
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 $m = \frac{2}{n(n+1)}$ ...
0
votes
0answers
25 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, ...
0
votes
1answer
15 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 ...
0
votes
2answers
20 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.
0
votes
1answer
36 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?
0
votes
1answer
27 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,\...
1
vote
0answers
33 views
0
votes
0answers
21 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
votes
1answer
43 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
votes
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 ...
0
votes
3answers
61 views

Explain why the slope of the equation is defined only for nonzero values of $b$. What happens when $b$ is zero?

Consider the equation $ax+by=c$ in 2-space and the slope for that equation where $a$ and $b$ are real numbers. Explain why the slope of the equation is defined only for nonzero values of $b$. ...
0
votes
2answers
38 views

Consider the equation $ax + by = c$ in 2-space and the slope for that equation where $a$ and $b$ are real numbers.

Consider the equation $ax + by = c$ in 2-space and the slope for that equation where a and b are real numbers. Explain using multiple representations why it is equivalent to say that a linear ...
0
votes
2answers
75 views

Finding value(s) for x where the tangent line of f(x) has a slope of 4.

I have this equation $\frac{3}{4}x^4 - 4x^3 + \frac{1}{2}x^2 + 7$ I am trying to find the value(s) for $x$ where the tangent line of $f(x)$ has a slope of 4. So I take my first derivative which I ...
0
votes
2answers
19 views

How do significant figures work in a cross unit division?

In one of my problems, I needed to find a slope on a graph with different units in physics. 309 cm² - 0.0 cm² / 100 cm - 0.0 cm The answer is A = 3.09 r² with A being area and r² being radius ...
0
votes
0answers
10 views

Decrease Beta bewteen to variables

I have two time series of return data. One is global equity and one is a seperate stock. I would like to know if there is a theoretical way of decreasing the EQ Beta of the stock? To be more clear: ...
0
votes
0answers
24 views

Slope and Expected Value of Percentile Ranks

Looking for help with this problem: Assume a child's expected income percentile is a linear function of their parents' income percentile. It turns out the intercept is enough to deduce the slope. If ...
0
votes
1answer
73 views

A line in the xy-plane contains the points (5, 4) and (2, –1)

Question: "A line in the $xy$-plane contains the points $(5, 4)$ and $(2, –1)$. Which is bigger: a) the slope of the line or b) $0$." Result: They draw out the figure and say "you can see that the ...
0
votes
0answers
19 views

How to measure the rate of decrease or increase of a particular stock in a specific time period

I need to measure the drop or increase of the value of a stock within a specific time frame. For example given a company XYZ, I need a formula to calculate the percentage change in value for stock XYZ ...
9
votes
1answer
118 views

If $\sigma: \mathbb{R}\to \mathbb{R}^2$ is a function that spirals,goes to infinity and repeats itself, then is $\sigma$ non-injetive?

Let $\sigma:\mathbb{R}\to \mathbb{R}^2$ be a smooth function such that $$\frac{\text{d}\sigma}{\text{d}t}(s) \neq 0, \quad \forall s \in \mathbb{R},$$ and $$\sigma(t+n) = \sigma(n) +\sigma(t),\ \...
0
votes
0answers
203 views

find root-mean-square (RMS) of sawtooth waveform

bipolar sawtooth I just want to make sure that I am right or not. I have to find Vrms of bipolar sawtooth waveform. The equation of RMS is RMS equation Slope I = Y1 = 0 X1 = 0 Y2 = 3 X2 = 0.25 X(t)...
1
vote
2answers
125 views

How to find point in Descartes Folium with slope of -1/3?

I stumbled upon a problem in my calculus book that asked to find the point in $x^3 + y^3 = 3xy$ that had a slope perpendicualr to $y = 3x + 1$ and also was in the first quadrant. I began by getting ...