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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Definition: Negligible compared to unity

It is often stated that if the slope or rotation of a point or an object is small then the derivative is negligible compared to unity. What does it mean? What is meant here by "unity"?
user504068
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On applying the mean value theorem for multiple functions

Is there some rule about multiple functions(all continuous and differentiable in some specific interval) having their average slopes (as obtained using LMVT) be equal to the slope at the same point? As in, are the c-values of all functions in a…
harry
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Assuming Slope in Slope-Intercept Form [Clarification]

So when learning about slope-intercept form, the equation that was used looked like this: $y = 2x + 3$, it then displayed a graph where the slope was going up by two and across by one. What I need a bit of clarification on is that do we just assume…
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Finding the rate of change of an algebra equation

I'm trying to help my daughter with her math homework and after scouring google and websites I find I truly do not understand how to complete this even after going several different websites. The problem is 2y - 12x = 36 I need to understand how to…
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Why is the slope form written how it is?

So, I was recently reviewing slope. While doing some problems with the slope formula $m = {y_2 - y_1\over x_2 - x_1}$, I started thinking why it was that and not $m = {y_1 - y_2\over x_1 - x_2}$. Because point one and two are interchangeable, this…
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slope equation calculation for a line

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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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}$ Suppose a triangle we have traingle image here so when…
devpa
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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.
Donna
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Given, y=x^3 - 2x+3, Find the equation of the tangent at at x =2

I am having trouble with the following question: Given, $y=x^{3}-2x+3$, Find the equation of the tangent at at x =2. I tried doing $y_{2}-y_{1}=m(x_{2}-x_{1})$. Then I plugged 2 into the equation and got 7 which I used as my m value but I am not…
Timmy
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How to find slope intercept through parallel lines?

I'm working on a school project. I need the slope intercepts from each problem. The problems are: Through: (5, 1) parallel to y=1/5x-1 Through: (-1,-3) parallel to y=2x+4 And so a few others. I don't want them solved for me, I want a text only…
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What do the sign and the value of a slope tell us regarding the nature of the straight line?

What could be the minimum and maximum possible value for a slope of a straight line? Is it -1 to +1 ? What do the sign and the value tell us regarding the nature of the straight line?
user366312
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How do I graph a line when rise=x?

I have the inequality $x+3y<21$. I have rearranged to y-intercept form to give me $y<-x/3+7$. I must have missed something in learning to graph in this form because I'm very unsure on how to graph a line when slope =$x$.
Bec S
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Rate of change video rentals

I'm looking at this problem which says: Video rental for 1 day is \$1.99. Video rental for 2 days is \$2.99. Rate of change= $\frac{2.99-1.99}{2-1}=\frac{1.00}{1}=1$ Now the problem I have with this is doesn't that mean it cost 1 dollar to rent for…
kero
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Understanding the steepness of the slope of the average of two other slopes

I have a small dataset including some value in money, some number of people, and the average which is (total money/people). When I graph these variables agains an outcome, the slope of the "total money" is negative, the slope of the "people"…
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How and why is Rise/Run gives the inclination of the line (or slope)?

How and why is Rise/Run gives the inclination of the line (or slope)? How to understand the theoratical concept behind it ?