# Find the Slope and Y-Intercept (6,-1) , (-21,17) (6,-1) , (-21,17)
Find the value of the slope.
Slope is equal to the change in y over the change in x, or rise over run.
m=change in ychange in x
The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).
m=y2-y1x2-x1
Substitute in the values of x and y into the equation to find the slope.
m=17-(-1)-21-(6)
Simplify.
Simplify the numerator.
Multiply -1 by -1.
m=17+1-21-(6)
m=18-21-(6)
m=18-21-(6)
Simplify the denominator.
Multiply -1 by 6.
m=18-21-6
Subtract 6 from -21.
m=18-27
m=18-27
Reduce the expression by cancelling the common factors.
Cancel the common factor of 18 and -27.
Factor 9 out of 18.
m=9(2)-27
Cancel the common factors.
Factor 9 out of -27.
m=9⋅29⋅-3
Cancel the common factor.
m=9⋅29⋅-3
Rewrite the expression.
m=2-3
m=2-3
m=2-3
Move the negative in front of the fraction.
m=-23
m=-23
m=-23
m=-23
Find the value of the y-intercept.
Substitute the value of m into the slope-intercept form of the equation, y=mx+b.
y=(-23)⋅x+b
Substitute the value of x into the slope-intercept form of the equation, y=mx+b.
y=(-23)⋅(6)+b
Substitute the value of y into the slope-intercept form of the equation, y=mx+b.
-1=(-23)⋅(6)+b
Rewrite the equation as (-23)⋅(6)+b=-1.
(-23)⋅(6)+b=-1
Simplify each term.
Cancel the common factor of 3.
Move the leading negative in -23 into the numerator.
-23⋅6+b=-1
Factor 3 out of 6.
-23⋅(3(2))+b=-1
Cancel the common factor.
-23⋅(3⋅2)+b=-1
Rewrite the expression.
-2⋅2+b=-1
-2⋅2+b=-1
Multiply -2 by 2.
-4+b=-1
-4+b=-1
Move all terms not containing b to the right side of the equation.
Add 4 to both sides of the equation.
b=-1+4
b=3
b=3
b=3
The values of the slope and y-intercept are m=-23 and b=3.
m=-23
b=3
Find the Slope and Y-Intercept (6,-1) , (-21,17)     