Question

Which of the following equations describes a line that passes through the points(-4, 4) and (2, 12)?

A. y= 4/3x + 28/3

B. y=-4/3x - -4/3

C. y= -4x - 12

D y= -8x-28

Answer 1

The equation of a line that passes through the points(-4, 4) and (2, 12) will be:

• y = 4/3x + 28/3

Hence, option A is true.

Explanation:

The slope-intercept form of the line equation

`y = mx+b`

where

• m is the slope

• b is the y-intercept

Given the points

• (-4, 4)

• (2, 12)

Finding the slope between (-4, 4) and (2, 12)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(-4,\:4\right),\:\left(x_2,\:y_2\right)=\left(2,\:12\right)`

`m=(12-4)/(2-\left(-4\right))`

`m=(4)/(3)`

Thus, the slope of the line m = 4/3

substituting (-4, 4) and m = 4/3 in the slope-intercept form of the line equation to determine the y-intercept b

y = mx+b

`4=(4)/(3)\left(-4\right)+b`

switch sides

`(4)/(3)\left(-4\right)+b=4`

`-(16)/(3)+b=4`

Add 16 to both sides

`-(16)/(3)+b+(16)/(3)=4+(16)/(3)`

`b=(28)/(3)`

Thus, the y-intercept b = 28/3

now substituting b = 28/3 and m = 4/3 in the slope-intercept form of the line equation

y = mx+b

y = 4/3x + 28/3

Therefore, the equation of a line that passes through the points(-4, 4) and (2, 12) will be:

• y = 4/3x + 28/3

Hence, option A is true.