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/run}}}

Examples:
{{{y=2x}}} the slope is {{{2}}} or {{{2/1}}}
The slope goes up 2 and to the right 1.

{{{graph(400,400,-20,20,-10,10,2x)}}}

{{{y=(3/4)x}}} the slope is{{{3/4}}}
The slope goes up 3 and to the right 4

{{{graph(400,400,-20,20,-10,10,(3/4)x)}}}

{{{y=-5x}}} the slope is {{{-5}}} or {{{(-5)/1}}}
The slope goes down 5 and to the right 1.

{{{graph(400,400,-20,20,-10,10,-5x)}}}

{{{y=(-7/2)x}}} the slope is {{{(-7)/2}}}
The slope goes down 7 and to the right 2.

{{{graph(400,400,-20,20,-10,10,(-7/2)x)}}}

How to find m given 2 points:

When you are asked to find slope you will be given 2 points.
{{{(x^1y^1)(x^2y^2)}}}
To find slope you use the equation:
{{{(y^2-y^1)/(x^2-x^1)}}}

Examples:

Given:(3,5)(0,2)
{{{(2-5)/(0-3)=(-3)/(-3)=1}}}
The slope is {{{1}}} or {{{1/1}}}.
The equation is {{{y=1x}}} or {{{y=x}}}.
{{{graph(300,300,-10,10,-10,10,x)}}}

Given:(-4,7)(1,-2)
{{{(-2-7)/(1-(-4))=(-9)/(5)}}}
The slope is {{{(-9)/5}}}.
The equation is {{{y=(-9/5)x}}}
{{{graph(300,300,-20,20,-20,20,((-9)/5)x)}}}

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(300,300,-10,10,-10,10,x+2)}}}
y=x+5
The y intercept is (0,5)
{{{graph(300,300,-10,10,-10,10,x+5)}}}
y=x-3
The y intercept is (0,-3).
{{{graph(300,300,-10,10,-10,10,x-3)}}}
y=x
When there is no b, the y intercept is (0,0).
{{{graph(300,300,-10,10,-10,10,x)}}}

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+b}}}
Plug the point into the equation and solve for b.
{{{4=2(1)+b}}}
{{{2=b}}}
The y intercept is (0,2).

Find the y intercept given y=3/5x and (5,-6).
{{{y=(3/5)x+b}}}
{{{-6=(3/5)5+b}}}
{{{-6=3+b}}}
{{{-9=b}}}
The y intercept is (0,-9).