Question

Which equation is the equation of a line that is perpendicular to x + 2y = 16?

Group of answer choices

y=−12x+6

y=12x−3

y=2x−2

y=−2x+8

Answer 1

`y=2x-2`

Explanation:

Hi there!

Linear equations are typically organized in slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when x=0)

Perpendicular lines always have slopes that are negative reciprocals. For example, 2 and -1/2. 3/4 and -4/3.

To determine whether a line is perpendicular to
`x + 2y = 16`, we must first determine its slope. Rearrange the given equation into slope-intercept form:

`x + 2y = 16\\\\2y =-x+ 16\\\\y=\displaystyle -(1)/(2)x +(16)/(2) \\\\y=\displaystyle -(1)/(2)x +8`

From this, we can clearly tell that the slope (m) of the line is
`\displaystyle -(1)/(2)`.

The negative reciprocal of
`\displaystyle -(1)/(2)` is 2. Therefore, the slope of a perpendicular line would be 2.

Therefore, the correct answer option would be
`y=2x-2`.

I hope this helps!