Question

What is an equation of the line that passes through the point (1,-3) and is perpendicular to the line x+3y=21, equation must start with y

Answer 1

`y=3x-6`

Explanation:

Given equation of a line:

`x+3y=21`

Rearrange the given equation to make y the subject:

`\implies x+3y=21`

`\implies 3y=-x+21`

`\implies y=-(1)/(3)x+7`

If two lines are perpendicular to each other, their slopes are negative reciprocals.

Therefore, the slope of the perpendicular line is 3.

`\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}`

Substitute the found slope and the given point (1, -3) into the point-slope formula:

`\implies y-(-3)=3(x-1)`

`\implies y+3=3x-3`

`\implies y=3x-6`