# Find the Slope and Y-Intercept (4,5) , (1,0) (4,5) , (1,0)
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=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
Find the value of the y-intercept.
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
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