Question

Find the equation of the line through (-5, 2)and perpendicular to the line y = -x + 3.+ 3Put in slope-intercept form.1=2

Answer 1

Given:

The point (-5, 2).

The line,

`y=(1)/(2)x+3`

To find the equation of the line through (-5,2) and perpendicular to the above line:

Since, the slope of the above line is,

`m=(1)/(2)`

So, the perpendicular slope is,

`m_1=-2`

Using point-slope formula,

`y-y_1=m(x-x_1)`

So, we get

`\begin{gathered} y-2=-2(x-(-5)) \\ y-2=-2(x+5) \\ y-2=-2x-10 \\ y=-2x-10+2 \\ y=-2x-8 \end{gathered}`

Hence, the slope intercept form of the line is,

`y=-2x-8`