Question

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

Answer 1

Answer:

$y=2x-2$

Step-by-step 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:

$x + 2y = 16\\\\2y =-x+ 16\\\\y=\displaystyle -\frac{1}{2}x +\frac{16}{2} \\\\y=\displaystyle -\frac{1}{2}x +8$

From this, we can clearly tell that the slope (m) of the line is $\displaystyle -\frac{1}{2}$.

The negative reciprocal of $\displaystyle -\frac{1}{2}$ 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!