Question

Write the equation of a line in slope-intercept form passing through (4, 5) and (6, 8)
A. y equals two-thirds x plus seven-thirds
B. y equals three-halves x plus 11
C. y equals three-halves x minus 1
D. y equals three-halves minus 8

Answer 1

It would be C use the slope intercept formula y=mx+b

Answer 2

The equation of a line is (y-y1) = m(x-x1)

You can find m with the slope formula m = (y2-y1)/(x2-x1) = rise / run

Let's find m first.
m = (8-5)/(6-4) = 3/2

Next plug in the values to the equation of a line
y - 5 = 3/2 (x - 4)
y = 3/2 x - 6 + 5
y = 3/2 x - 1