Question

Write an equation for the following condition:
Perpendicular to y= -3x+7, through (3,5)

Answer 1

So the equation: y= -3x+7 has a slope of -3. The question is asking for a line that is perpendicular to that line, which means the new slope must be inverse negative

So, new slope: 1/3

Use the point (3,5)

Now use the point slope formula

y-y1=m(x-x1)

y-5=1/3(x-3)

Now solve for y in the following equation: y-5=1/3(x-3)

y=1/3x+4.

Therefore the equation for a perpendicular line to y= -3x+7, and that goes through the point (3,5), is :
y=1/3x+4.