Question

Find the equation of a line passing through (-7,7) perpendicular to y= -5/2x-2

Answer 1

2x-5y=-49.

Step-by-step explanation:

Given the line:

`y=-(5)/(2)x-2`

Comparing with the slope-intercept form: y=mx+b

`\text{Slope,m}=-(5)/(2)`

Two lines are perpendicular if the product of their slopes is -1.

Let the slope of the new line =n.

`\begin{gathered} n*-(5)/(2)=-1 \\ n=(2)/(5) \end{gathered}`

Therefore, the equation of the perpendicular line passing through (-7,7) is:

`\begin{gathered} y-y_1=m(x-x_1) \\ y-7=(2)/(5)(x-(-7)) \\ y-7=(2)/(5)(x+7) \\ 5(y-7)=2(x+7) \\ 5y-35=2x+14 \\ 2x-5y=-35-14 \\ 2x-5y=-49 \end{gathered}`

The equation of the line is 2x-5y=-49.