Question

Write the equation of the line perpendicular to y=1/7x-3 and passing through (-3,2)

Answer 1

The equation of a line perpendicular to y is

`y=-7x+b`

where b is a constant hitherto unknown.

However, we also know that this perpendicular line passes through (-3,2); therefore, the above equation must satisfy y(-3) = 2.

Putting x = -3 into the above equation gives us

`y(-3)=-7(-3)+b=2`
`21+b=2`
`\therefore b=-19`

Hence, the equation perpendicular to y = 1/7x-3 which passes through (-3, 2) is

`\textcolor{#FF7968}{y=-7x-19}\text{\textcolor{#FF7968}{.}}`