# Questions tagged [slope]

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

217 questions
2answers
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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 ...
1answer
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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 ...
1answer
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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 ...
2answers
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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 ...
1answer
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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 ...
1answer
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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, ...
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 ...
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 ...
0answers
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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-$\frac{y1-y2}{slope}$ ...
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 ...
1answer
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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 ...
1answer
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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 ...
4answers
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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= $\frac{\Delta X} {\Delta Y}$ ?
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 ...
3answers
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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 ...
3answers
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### 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 ...
3answers
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1answer
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### 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 ...
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.
1answer
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### 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?
1answer
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0answers
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### 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 ...