# Find the Slope and Y-Intercept (4,3) , (1,5) (4,3) , (1,5)
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=5-(3)1-(4)
Simplify.
Simplify the numerator.
Multiply -1 by 3.
m=5-31-(4)
Subtract 3 from 5.
m=21-(4)
m=21-(4)
Simplify the denominator.
Multiply -1 by 4.
m=21-4
Subtract 4 from 1.
m=2-3
m=2-3
Move the negative in front of the fraction.
m=-23
m=-23
m=-23
Find the value of the y-intercept.
Substitute the value of m into the slope-intercept form of the equation, y=mx+b.
y=(-23)⋅x+b
Substitute the value of x into the slope-intercept form of the equation, y=mx+b.
y=(-23)⋅(4)+b
Substitute the value of y into the slope-intercept form of the equation, y=mx+b.
3=(-23)⋅(4)+b
Rewrite the equation as (-23)⋅(4)+b=3.
(-23)⋅(4)+b=3
Simplify each term.
Multiply (-23)(4).
Multiply 4 by -1.
-4(23)+b=3
Combine -4 and 23.
-4⋅23+b=3
Multiply -4 by 2.
-83+b=3
-83+b=3
Move the negative in front of the fraction.
-83+b=3
-83+b=3
Move all terms not containing b to the right side of the equation.
Add 83 to both sides of the equation.
b=3+83
To write 3 as a fraction with a common denominator, multiply by 33.
b=3⋅33+83
Combine 3 and 33.
b=3⋅33+83
Combine the numerators over the common denominator.
b=3⋅3+83
Simplify the numerator.
Multiply 3 by 3.
b=9+83
Add 9 and 8.
b=173
b=173
b=173
b=173
The values of the slope and y-intercept are m=-23 and b=173.
m=-23
b=173
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