# 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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### Find a tangent line on a function equal to a specific slope [closed]

Find the tangent line on $f(x)=x^2$ which runs parallel to the slope of $y=2x+6$.
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### Regarding the calculation of the slope of a tangent.

I have recently had some of my first lessons in calculus. We've learned to use the well-known formula for the slope of a tangent: $$m_t=\lim_{h\to 0}\frac{f(a+h)-f(a)}{h}$$ When working with this ...
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### How to interpret the slope in this chart?

I have a chart that was generated from a linear regression. It looks like this: I see that it's slope is slightly down. The slope I get from the linear regression, however is -1.3081201334816588E-9 ...
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### Finding the normal to a curve of an implicit function using differentiation

The question asks to find the tangent and normal to the curve of the following equation at the point ($\sqrt3, 2$): $$x^2-\sqrt{3}xy+2y^2=5$$ I began by finding the first derivative of this, ...
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### slope equation calculation for a line [duplicate]

when slope m=0 it is a straight horizontal line and when slope is vertical line..I mean what is the value for slope m to get vertical line?I think that for vertical line, slope is m=0 also.
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### Total Cost According to Miles Driven [closed]

A computer repair person charges 50.00 dollars per hour, plus an additional mileage fee. The charge for mileage varies directly with the square root of the number of miles traveled. If one hour plus ...
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### Using slopes to find orthocentre of a triangle

Let vertices of a triangle be $A(1,0)$, $B(-2,1)$, $C(5,2)$. Let orthocentre be $H(a,b)$. Slope of $AH=b/(a-1)$, slope of $BH = (b-1)/(a+2)$, slope of $CH = (b-2)/(a-5)$. I assumed $AH, BH, CH$ to be ...
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### Why did this method gave the orthocentre of the triangle?

Coordinates of vertices of a triangle are given(say $A$, $B$, $C$). I assumed coordinates of orthocenter to be $H(a, b)$. I calculated slope of $AH, BH, CH$ in terms of $a$ and $b$. For some reason I ...
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### Average Rate of Change From Graph

I'm doing my pre-calculus homework and I cannot find an answer to this problem in my book or anywhere. I am give the following graph The question is the following: Estimate the average rate of ...
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### What characterizes a tangent line?

If the traditional way to define the tangent line to a curve $f(x)$ through the point say $(a , f(a))$ is: ( the tangent line through the point $(a ,f(a))$ is the line that passes through this point ...
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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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### 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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### 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 ...
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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### (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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### 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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### 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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### 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 ...
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 ...