105k views
2 votes
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

1 Answer

3 votes

Answer:


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

What is an equation of the line that passes through the point (1,-3) and is perpendicular-example-1
User Samo Jerom
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories