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

For the equation given:

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

for perpendicular lines, the relationship between their slopes is given by:

`m _(1) * m _(2) = - 1`

m1 is slope for one line, and m2 is slope for another line.

`- (1)/(2) * m_(2) = - 1 \\ \\ m_(2) = - 1 * - 2 \\ { \underline{ \: \: m_(2) = 2 \: \: }}`

Therefore, equation is;

`{ \boxed{ \boxed{y = 2x - 2}}}`