(4,5) , (1,0)

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=0-(5)1-(4)

Simplify.

Simplify the numerator.

Multiply -1 by 5.

m=0-51-(4)

Subtract 5 from 0.

m=-51-(4)

m=-51-(4)

Simplify the denominator.

Multiply -1 by 4.

m=-51-4

Subtract 4 from 1.

m=-5-3

m=-5-3

Dividing two negative values results in a positive value.

m=53

m=53

m=53

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

y=(53)x+b

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

y=(53)⋅(4)+b

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

5=(53)⋅(4)+b

Rewrite the equation as (53)⋅(4)+b=5.

(53)⋅(4)+b=5

Multiply (53)(4).

Combine 53 and 4.

5⋅43+b=5

Multiply 5 by 4.

203+b=5

203+b=5

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

Subtract 203 from both sides of the equation.

b=5-203

To write 5 as a fraction with a common denominator, multiply by 33.

b=5⋅33-203

Combine 5 and 33.

b=5⋅33-203

Combine the numerators over the common denominator.

b=5⋅3-203

Simplify the numerator.

Multiply 5 by 3.

b=15-203

Subtract 20 from 15.

b=-53

b=-53

Move the negative in front of the fraction.

b=-53

b=-53

b=-53

The values of the slope and y-intercept are m=53 and b=-53.

m=53

b=-53

Find the Slope and Y-Intercept (4,5) , (1,0)