What is the slope-intercept form of the equation of the line that passes through the points
(-3, 2) and (1, 5) ?
a. y=3/4x−7/4
b. y=3/4x−9/2
c. y=3/4x+7/2
d. y=3/4x+17/4

d. y = 3/4x + 17/4.

To write the slope-intercept form y = mx + b of a line passing through (-3, 2) and (1,5).

First, we have to calculate the slope m.

m = (y₂-y₁)/(x₂-x₁), with (x₁, y₁) = (-3, 2) and (x₂, y₂) = (1, 5)

m = (5 - 2)/(1 - (-3))

m = 3/4

Second, we have to find the y-intercept.

y = mx + b, where m is the slope and b is the y-intercept.

Using one of the two ordered pair and plug it in for x and y in the equation y = mx + b.

Taking the ordered pair (1, 5):

5 = 3/4 (1) + b

5 = 3/4 + b

Solving for b

b = 5 - 3/4

b = [5(4) - 3(1)]/4

b = (20 - 3)/4

b = 17/4

Finally, write down the slope-intercept equation of the form y = mx + b, with m = 3/4 and b = 17/4:

y = mx + b

y = 3/4x + 17/4