Question

Write the equation of the line passing through (-3,1) that is perpendicular to 3x-8y=16

Answer 1

two lines are perpendicular when their slope is inverted and have the opposite sign

the general form of the equation line is-3,1

`y=mx+b`

where m is the slope

rewrite

`\begin{gathered} 3x-8y=16 \\ 3x-16=8y \\ y=(3x-16)/(8) \\ y=(3)/(8)x-2 \end{gathered}`

so, the slope 3/8

the slope of the other line is

`(3)/(8)\longrightarrow-(8)/(3)`

to write the new equation of the line we use the slope and replace the point (-3,1)

`\begin{gathered} (1)=(-(8)/(3))(-3)+b \\ 1=8+b \\ b=-7 \end{gathered}`

now, replace b and the slope to create the line

`y=-(8)/(3)x-7`