Mathematics Stack Exchange
Mathematics 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.

In mathematics, the slope (or gradient) of a line is a number that describes both the direction and the steepness of the line. In the US and a few other countries the slop is denoted by the letter $m$ in the slope-intercept form of a line, $y=mx+b$.

Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line. A line that is decreasing has a negative "rise". The line may be practical - as set by a road surveyor, or in a diagram that models a road or a roof either as a description or as a plan.

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Average Rate of Change of Functions

In here to find out the average rate of change -5 and 2 were used. But I'm wondering why, because in the interval these aren't included. Wouldn't it only be correct using -5 and -2 to solve the problem if the interval was -5<=x<=-2?
Steve
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Is there a correct mathematical term for the inverse of the slope?

Linear graphs all have a slope that can be calculated by deviding the progress on the y-axis by the progress on the x-axis. Is there a correct term to refer to the inverse of the slope, that means the progress on the x-axis devided by the progress…
Michelle_B
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How to write an equation of a line bisecting an angle in terms of the slope of the bisector.

I have two lines $y-8=\dfrac{-1}{7}(x+6)$ $y-8=\dfrac{-1}{2}(x+6)$ They both intersect at point $(-6,8)$. I'm trying to find the slope of the line that bisects these two lines. In this question, there was an equation for the line of the angle…
Christopher Gaston
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How fast is the tree growing?

This information is given: Mrs. Fitzgerald planted a tree. After 10 days, the tree measured 39 inches tall. After 28 days, the tree measured 51 inches tall. This is what I did: Since we are given two points, I found the slope. To find slope between…
thatweirdpandanextdoor
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Calculate slope for 5 data points with no specific X value

I'd like to easily find out if the five points are getting better, worse, or staying flat. This is in regard to performance of a machine learning classifier when the classifier is provided fractions of training data. So for example the fractions…
There
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Finite range of a map $\rho: \mathbb{Z} \rightarrow \mathbb{Z}$

Let $\rho: \mathbb{Z} \rightarrow \mathbb{Z}$ is a map with the property: $E^{+}_{\rho} = \{\rho(m + n) - \rho(m) - \rho(n) \in \mathbb{Z} \mid m,n \in \mathbb{N}\}$ is a finite set and $\rho(-n) = -\rho(n)$ for all $n \in \mathbb{Z}$. We call such…
Chau Long
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Find the equation of the normal line

Find the equation of the normal line to curve $y=2x^2+3$ that is perpendicular to the line $8x-y+3=0$ I have already solved the $m = 8$, $m'= -\frac{1}{8}$. But I don't know how to solve for the $x,y$ points.
Suan Suan
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Simple math, not sure what it is accomplishing (line segment intersection)

The problem of line segment intersection seems simple enough using orientation, but the explanation in this blog leading up to formula used says one thing, and the math used is doing another. The solution involves determining if three points are…
Lanet Rino
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Slope of the equation $ y(8-x)= 1 $

The curve $xy =1$ has a slope that is negative everywhere in the first quadrant. This is apparent both visually and algebraically ($dy/dx = -y/x$). Its reflection in the line $x=4$ is the curve $y(8-x) = 1$ (Reflection of rectangular hyperbola in…
phil342
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What is the slope of a line half way between two lines of slope m1 and m2?

I have two lines of slope m1 and m2 respectively. What is the slope of the line bisecting these two lines? Clearly there are 2 different lines which can be constructed, one perpendicular to the other. I am looking for the one which bisects the…
Adrian
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Generate $x$ values using start and end points using Slope equation/formula

I know the start and the end points of a slope.How do I get all the $(x,y)$ values between the start and end point. For example: When $x = 0$, $y = 5$ and $x = 20000$, $y = 20$. How do I generate the $y$ values when $x$ ranges from $0$ to $20000$?
VK_217
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What is the meaning of normalization (in this specific context)?

Though I want to address a specific aspect which is about normalization I also would like to see short answers/reasons about the purpose of normalization. Maybe this will answer the next: I got thousands of diodes to analyze which are mainly…
Ben
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What is the 'slope' of a function that has x, instead of y as the subject, called?

We are all familiar with y = mx + b, the slope-intercept form with y as the subject: m is the gradient - how much y changes by an increase in x of 1. b is the y-intercept - the value of y at x = 0. Now, this equation can also be represented…
RexSir9001
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Points on a line distant from a given point on the line

I have a line with slope given as the pair: dx, dy (slope: dy/dx). Given a point (x, y) on the line, what are the coordinates (x(d), y(d)) of the 2 points such that the distance from (x,y) measured on that line is equal to d (where d is any positive…
Jada
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How to Compute the Point Slope?

Assume I have points $(125,1)$ and $(5000,20)$. The slope would be $m = \frac{y_2 - y_1} { x_2 - x_1}$ or $256.5789474$, right? Assume the slope and one point are known, I should be able to compute the y value for a given $x$ using the point slope…
MathNewbie
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