Find a line perpendicular to the line 3x-y+4=0 passing through (-2,2)??

Question

At first I got y=1/3x+2 2/3 then I tried the probelm again and I got y=1/3x+2. When it says perpendicular does that mean the lines have to cross at a 90 degree angle??? because I don't think either one of my answers do that. I am so confused!!! help!!!

Answer 1

Yes, perpendicular lines must intersect at a 90 degree angle. If you rearrange your original equation into the slope-intercept form, y=mx + b, you will get a slope of 3 (Remember to multiply both sides by -1 as you will get -y = -3x - 4 to start with.) What Jared said about the slope of the perpendicular line being a negative reciprocal is correct, so the slope of your new line will be -1/3.
Substitute the points of intersection with the new slope in the y=mx + b equation so that you can find the y-intercept of the new line.
2 = -1/3(-2) + b
If you need to write your answer in standard form, substitute the new slope (-1/3) and your new y-int into the y=mx + b formula and rearrange it.

Hope that helps.

Answer 2

Perpendicular lines must be at 90 degrees with respect to each other.
As for the relation of their slopes, the slope of the 2nd line is the negative reciprocal of the slope of the 1st line:

m2 = -(1/m1)

For the given equation 3x-y+4=0, the slope (m1) = 3
Given the above relation, the slope of the 2nd line (m2) = -1/3

Using the slope intercept form, y = mx + b, you can substitute the value of m2 and the given point (-2,2) to solve for b:

y = mx + b
2 = (-1/3)*(-2) + b
b = 1 1/3

Giving you the equation: y = -1/3 x + 1 1/3

Answer 3

perpendicular means both lines have OPPOSITE RECIPROCAL slopes

for example 2/3 and -3/2

so find the slope of the first line and the opposite reciprocal is M of the line you're looking for

y = mx + b

then if (-2,2) is the intersection point....then -2 = x and 2 = y

2 = M(-2) + b (at that point you'd have solved what m is since m is the opposite reciprocal of m in the line you're given)

so you can solve for me....and put y and x back in and you're done