Question

Find the equation of line b in slope intercept formLine a is perpendicular to line bLine a passes through the point (1,-4) and (9,-6)Line b passes through the point (-6,-24)

Answer 1

First, we need to find the slope of line a, using the next formula

`m=(y_2-y_1)/(x_2-x_1)`

where

(1,-4)=(x1,y1)

(9,-6)=(x2,y2)

we substitute the values

`m=(-6+4)/(9-1)=(-2)/(8)=-(1)/(4)`

The slope of a perpendicular line to line a is the inverse of the slope we found therefore the slope of line b will be

`m_b=4`

then we will use the slope-point form to find the equation of line b

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

where

(-6,-24)=(x1,y1)

`y+24=4(x+6)`

then in order to find the equation in the slope-intercept form, we need to isolate the y

`\begin{gathered} y+24=4x+24 \\ \end{gathered}`
`y=4x+24-24`
`y=4x`

The equation of line b is y=4x