(12,-5) , (-7,-3)

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

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

Find the Slope and Y-Intercept (12,-5) , (-7,-3)