Equation of line perp. to x - 7y = 9 through (3, -4)

[silverdragon316]

This is my problem:

Find an equation of the line perpendicular to x - 7y = 9 containing the point (3, -4)

x - 7y = 9
..-7y = -x + 9
.....y = (1/7)x - 9/7

.....Y - Y₁ = m(X - X₁)
...Y - (-4) = -7(x - 3)
......Y + 3 = -7(x - 3)
......y + 3 = -7x + 21
..........y = -7x + 18

So, then the equation of the perpendicular line is y = -7x + 18 ?
If not, where did I go wrong?

 

[galactus]

You replaced 4 with 3. It should be y=-7x+17

You solved for \(\displaystyle y=\frac{1}{7}x-\frac{9}{7}\)

Therefore, the perp slope is -7

Use y=mx+b:

-4=-7(3)+b

b=17

y=-7x+17