# Find the Slope and Y-Intercept (12,-5) , (-7,-3) (12,-5) , (-7,-3)
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=-3-(-5)-7-(12)
Simplify.
Simplify the numerator.
Multiply -1 by -5.
m=-3+5-7-(12)
Add -3 and 5.
m=2-7-(12)
m=2-7-(12)
Simplify the denominator.
Multiply -1 by 12.
m=2-7-12
Subtract 12 from -7.
m=2-19
m=2-19
Move the negative in front of the fraction.
m=-219
m=-219
m=-219
Find the value of the y-intercept.
Substitute the value of m into the slope-intercept form of the equation, y=mx+b.
y=(-219)⋅x+b
Substitute the value of x into the slope-intercept form of the equation, y=mx+b.
y=(-219)⋅(12)+b
Substitute the value of y into the slope-intercept form of the equation, y=mx+b.
-5=(-219)⋅(12)+b
Rewrite the equation as (-219)⋅(12)+b=-5.
(-219)⋅(12)+b=-5
Simplify each term.
Multiply (-219)(12).
Multiply 12 by -1.
-12(219)+b=-5
Combine -12 and 219.
-12⋅219+b=-5
Multiply -12 by 2.
-2419+b=-5
-2419+b=-5
Move the negative in front of the fraction.
-2419+b=-5
-2419+b=-5
Move all terms not containing b to the right side of the equation.
Add 2419 to both sides of the equation.
b=-5+2419
To write -5 as a fraction with a common denominator, multiply by 1919.
b=-5⋅1919+2419
Combine -5 and 1919.
b=-5⋅1919+2419
Combine the numerators over the common denominator.
b=-5⋅19+2419
Simplify the numerator.
Multiply -5 by 19.
b=-95+2419
Add -95 and 24.
b=-7119
b=-7119
Move the negative in front of the fraction.
b=-7119
b=-7119
b=-7119
The values of the slope and y-intercept are m=-219 and b=-7119.
m=-219
b=-7119
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