Question

What is an equation of the line that is perpendicular to -x+3y=9 and passes through the point (-3,2)

Answer 1

Answer:

y=-3x-7

Step-by-step explanation:

the line is currently in standard form (ax+by=c). Let's put it into slope-intercept form (y=mx+b)

-x+3y=9

add x to both sides

3y=x+9

divide by 3

y=1/3x+3

perpendicular lines have slopes that when multiplied, equal -1.

to find the slope (m) of our new line:

1/3m=-1

multiply by 3

m=-3

the slope of the new line is -3

here's our equation so far:

y=-3x+b

we need to find b (y intecept)

since the line passes through the point (-3,2), it should be a solution in the equation (plug it in, and the result is a true statement). We can also use it to find b

so, substitute the pointt into the equation:

2=-3(-3)+b

multiply

2=9+b

subtract

-7=b

so the equation of the line is y=-3x-7

Hope this helps!