Question

What Is the equation in the slope- intercept form of the line that passes through (2,-2) and is perpendicular to the line resprsented by y= 2/5 x+2

Answer 1

The slope of line perpendicular to the line with slope m is -1/m.

The line y=2/5 x+2 is in the form of the equation y=mx+c.

So, comparing equations, we get

`m=(2)/(5)`

So, the slope of a line perpendicular to the line y= 2/5 x+2​ is

`m_1=(1)/(m)=(-1)/((2)/(5))=(-5)/(2)`

The slope intercept form for a line passing through the point (x1,y1) and having slope m1 is

`(y_1-y)/(x_1-x)=m_1`

The point given is

`(x_1,y_1)=(2,-2)`

Also the slope for the line is -5/2 as obtained above. So

`\begin{gathered} (-2-y)/(2-x)=(-5)/(2) \\ (-2-y)2=-5(2-x) \\ -4-2y=-10+5x \\ -4+10=5x+2y \\ 5x+2y=6 \end{gathered}`

The equation is 5x+2y=6.