A straight line in the coordinate plane passes through the...

points with (x,y) coordinates (–1,1) and (2,3). What are the
(x,y) coordinates of the point at which the line passes
through the y-axis?
A. (–2,0)
B. ( 0,2/3 )
C. ( 0, 5/3)
D. ( 0,2)
E. ( 0, 5/2)

Why is the answer C.?

slope m=(y2-y1)/(x2-x1)
m=(3-1)/(2-(-1))
m=2/3
Point-slope
(y-y1) = m (x - x1)
(y-3) = (2/3)(x - 2)
y-3=(2/3)x-(4/3)
y=(2/3)x-4/3+9/3
y=(2/3)x+5/3
this line is passing the y-axis when x=0
y=5/3
so the y-intercept (0,5/3)

Slope is rise over run

3-1 over 2 -(-1)
2/3

Plug in either point to get your line:
y = 2/3x + b
1 = -2/3 + b
5/3 = b

Line is

y = 2/3x + 5/3
(0,5/3) is on that line