Question

RWhich of the following lines is perpendicular to theequation given below?ICUy = -2x + 80 x – 2y = 62x + y = 4O 2x - y = 1x + 2y = 8

Answer 1

For two perpendicular lines, the product of the slopes equal -1, such that

`m_1* m_2=-1`

The main line's equation is given by

`y=-2x+8`

On comparing with the slope-intercept form of the equation of a line,

`y=mx+c`

The slope is given as -2.

Hence, the slope of the second line will be

`\begin{gathered} -2* m_2=-1 \\ m_2=(-1)/(-2) \\ m_2=(1)/(2) \end{gathered}`

Next, we check the options to find which has a slope equal to 1/2.

OPTION 1: x - 2y = 6

Rewriting in the slope-intercept form, we have

`\begin{gathered} -2y=-x+6 \\ \text{Dividing through by -2, we have} \\ y=(1)/(2)x-3 \end{gathered}`

Therefore, the slope of the line is 1/2.

Hence, the FIRST OPTION is correct.