Find the equation of the line through point (−1,2) and perpendicular to x+3y=3.

y=3x+5

Step-by-step explanation:

the equation x+3y=3 is in standard form (ax+by=c)

we can put it into slope intercept form (y=mx+b) to make it easier.

subtract x from both sides

3y=-x+3

divide by 3

y=-1/3x+1

Perpendicular lines have slopes that are opposite (one is negative and one is positive) and reciprocal, so if you mutiply them together, it will equal -1

use this equation:

-1/3m=-1

multiply by -3 on both sides

m=3

equation so far: y=3x+b (b is a placeholder)

since the equation passes through the point (-1,2), we can substitute it into the equation

2=3(-1)+b

2=-3+b

5=b

the equation is y=3x+5

Hope this helps!