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
