(4,3) , (1,5)

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-(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

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

Find the Slope and Y-Intercept (4,3) , (1,5)