Question

What is the equation in slope-intercept form of the line that passes through the points (−12, −4) and (4, 8)?

A. y = −43 − 20
A. , y = −43 − 20

B. y = 43 − 12
B. , y = 43 − 12

C. y = −0.75 − 13
C. , y = −0.75 − 13

D. y = 0.75x +5
D. , y = 0.75x +5

Answer 1

Choice D.
`y = 0.75\, x + 5`.

Explanation:

The general equation for the slope-intercept form of a line in a cartesian plane is
`y = m\, x + b`, where:

• 
  `m` is the slope of the line, and
• 
  `b` is the
  `y`-intercept of the line. (The
  `y\!`-intercept of a line in a cartesian plane is the
  `y\!\!`-coordinate of the point where the line intersects the
  `\! y \!`-axis.)

Start by finding the value of
`m`. The slope of a line is equal to its rise-over-run. For the two points in this question:

• The "rise" is the
  `y`-coordinate of the first point minus that of the second:
  `\text{rise} = (-4) - 8 = -12`.
• The "run" is the
  `x`-coordinate of the first point minus that of the second. The order of these two points should stay the same:
  `\text{run} = (-12) - 4 = -16`.

Calculate the slope of this line:

`\displaystyle m = \text{slope} = \frac{\text{rise}}{\text{run}} = (-12)/(-16) = 0.75`.

The equation of the line becomes:

`y = \underbrace{0.75}_(m)\, x + b`.

Substitute the coordinates of either of the two points to find
`b`. For example, for the first point
`(12, -4)`, substitute in the following:

• 
  `x = -12`, and
• 
  `y = -4`.

The equation becomes:

`-4 = 0.75 * (-12) + b`.

Solve for the value of
`b`:

`b = 5`.

Hence, the slope-intercept form of this line shall be:

`y = 0.75\, x + 5`.