What is the equation of the line, in slope-intercept form, that passes through (3, -1) and (-1, 5)?
a) y = - 3/2 x + 7/2
b) 2 y = -3 x + 7
c) 2 x + 3 y - 7 = 0

a) y = - 3/2 x + 7/2

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = y intercept

m represents the slope of the line.

m = (y2 - y1)/(x2 - x1)

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

The line passes through (3, - 1) and (- 1, 5),

y2 = 5

y1 = -1

x2 = - 1

x1 = 3

Slope,m = (5 - - 1)/(- 1 - 3) = 6/- 4 =

- 3/2

To determine the y intercept, we would substitute x = 3, y = - 1 and m= - 3/2 into y = mx + c. It becomes

- 1 = - 3/2 × 3 + c

- 1 = - 9/2 + c

c = - 1 + 9/2

c = 7/2

The equation becomes

y = - 3x/2 + 7/2