Find the equation of the line that passes through (-1, 4) and is perpendicular to the line that passes through (2, 2) and (4, - 4)

Question

(A) y = 3x + 7

(B) y = (-1/3)x + (1/3)

(C) y = (1/3)x + (13/3)

(D) y = -3x + 8

(E) None of the above

Answer 1

You will need to first find the slope from the two given points (2,2) and (4,-4) to then find the negative inverse.

I am old school, so I I like to graph my points and then use the "rise over run" formula to find my slope. After you plot both points, connect them to see how main points it went down (rise) and how many points it went over (run). You will see that you have to go down 6 points and over to the right 2 points to connect the dots.This causes a negative slope and will give you -6/2 which will simplify to a slope of -3.

Once you find the slope of -3, you will need to find the negative inverse of that which is just flipping the fraction upside down and changing negative to a positive. That would make the new slope 1/3.

Then finally you will use the point given to you (-1,4) and the slope you found to give you the equation to the new line. You will substitute the information you know with the y intercept slope formula to find the y intercept.

y=mx + b

Example:

y=4

m=1/3

x= -1

y=mx+b

4=1/3(-1) +b

4=-1/3+b

4+1/3=b

12/3+1/3=b

13/3=b

y=1/3x+13/3



Answer 2

First, find the slope of the line between the given points. Slope = m = (y2 - y1) / (x2 - x1)

m = (-4-2) / (4-2) = -3

A line perpendicular to this will have a slope that is the "negative inverse"--i.e. m = +1/3

Thus, in slope-intercept format, it will be:

y = x/3 + b

All that remains is to find b. To do that plug in the x and y values for the new point ( (-1,4) ), and solve for b