Lesson Finding the slope and y intercept

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In this lesson you will learn how to find the slope and the y intercept.

To start off, we will learn what m and b stand for in the equation y=mx+b.
m = slope
b = y intercept
The slope shows the slope of the line.
rise%2Frun

Examples:
y=2x the slope is 2 or 2%2F1
The slope goes up 2 and to the right 1.
graph%28400%2C400%2C-20%2C20%2C-10%2C10%2C2x%29
y=%283%2F4%29x the slope is3%2F4
The slope goes up 3 and to the right 4
graph%28400%2C400%2C-20%2C20%2C-10%2C10%2C%283%2F4%29x%29
y=-5x the slope is -5 or %28-5%29%2F1
The slope goes down 5 and to the right 1.
graph%28400%2C400%2C-20%2C20%2C-10%2C10%2C-5x%29
y=%28-7%2F2%29x the slope is %28-7%29%2F2
The slope goes down 7 and to the right 2.
graph%28400%2C400%2C-20%2C20%2C-10%2C10%2C%28-7%2F2%29x%29

How to find m given 2 points:

When you are asked to find slope you will be given 2 points.
%28x%5E1y%5E1%29%28x%5E2y%5E2%29
To find slope you use the equation:
%28y%5E2-y%5E1%29%2F%28x%5E2-x%5E1%29

Examples:
Given:(3,5)(0,2)
%282-5%29%2F%280-3%29=%28-3%29%2F%28-3%29=1
The slope is 1 or 1%2F1.
The equation is y=1x or y=x.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%29

Given:(-4,7)(1,-2)
%28-2-7%29%2F%281-%28-4%29%29=%28-9%29%2F%285%29
The slope is %28-9%29%2F5.
The equation is y=%28-9%2F5%29x
graph%28300%2C300%2C-20%2C20%2C-20%2C20%2C%28%28-9%29%2F5%29x%29

Now you know all about slope.

How to find b:

b stands for the y intercept.
y=mx+b
if b were 3, we would plot (0,3) and then graph the line.

Examples:(The slope will be 1 for these examples)
y=x+2
The y intercept is (0,2)
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%2B2%29
y=x+5
The y intercept is (0,5)
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%2B5%29
y=x-3
The y intercept is (0,-3).
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx-3%29
y=x
When there is no b, the y intercept is (0,0).
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%29
How to find b when given y=mx+b:

Sometimes you will be given an equation and a point and you will have to find b.

Example:
Find the y intercept given y=2x and (1,4).
y=2x%2Bb
Plug the point into the equation and solve for b.
4=2%281%29%2Bb
2=b
The y intercept is (0,2).

Find the y intercept given y=3/5x and (5,-6).
y=%283%2F5%29x%2Bb
-6=%283%2F5%295%2Bb
-6=3%2Bb
-9=b
The y intercept is (0,-9).
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