Answer:
[tex]y=3x-6[/tex]
Step-by-step explanation:
Given equation of a line:
[tex]x+3y=21[/tex]
Rearrange the given equation to make y the subject:
[tex]\implies x+3y=21[/tex]
[tex]\implies 3y=-x+21[/tex]
[tex]\implies y=-\dfrac{1}{3}x+7[/tex]
If two lines are perpendicular to each other, their slopes are negative reciprocals.
Therefore, the slope of the perpendicular line is 3.
[tex]\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}}[/tex]
Substitute the found slope and the given point (1, -3) into the point-slope formula:
[tex]\implies y-(-3)=3(x-1)[/tex]
[tex]\implies y+3=3x-3[/tex]
[tex]\implies y=3x-6[/tex]
