(-1,4) , (2,5)

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=5-(4)2-(-1)

Simplify.

Simplify the numerator.

Multiply -1 by 4.

m=5-42-(-1)

Subtract 4 from 5.

m=12-(-1)

m=12-(-1)

Simplify the denominator.

Multiply -1 by -1.

m=12+1

Add 2 and 1.

m=13

m=13

m=13

m=13

Substitute the value of m into the slope-intercept form of the equation, y=mx+b.

y=(13)x+b

Substitute the value of x into the slope-intercept form of the equation, y=mx+b.

y=(13)⋅(-1)+b

Substitute the value of y into the slope-intercept form of the equation, y=mx+b.

4=(13)⋅(-1)+b

Rewrite the equation as (13)⋅(-1)+b=4.

(13)⋅(-1)+b=4

Simplify each term.

Combine 13 and -1.

-13+b=4

Move the negative in front of the fraction.

-13+b=4

-13+b=4

Move all terms not containing b to the right side of the equation.

Add 13 to both sides of the equation.

b=4+13

To write 4 as a fraction with a common denominator, multiply by 33.

b=4⋅33+13

Combine 4 and 33.

b=4⋅33+13

Combine the numerators over the common denominator.

b=4⋅3+13

Simplify the numerator.

Multiply 4 by 3.

b=12+13

Add 12 and 1.

b=133

b=133

b=133

b=133

The values of the slope and y-intercept are m=13 and b=133.

m=13

b=133

Find the Slope and Y-Intercept (-1,4) , (2,5)