Which of the following lines is perpendicular to the line y = -3 x + 2 and passes through the point (–2, 8)?

Answer 1

Doug answered correctly, but I just wanted to show an alternative route you could have taken after finding your slope. This is what I have taught kids in the past.

So like Doug says your negative reciprocal is 1/3 (-3/1 has a reciprocal of -1/3 then take the negative/opposite of that and you get positive 1/3)

You can use slope intercept form to solve for your y-intercept and then put it back in slope-intercept form at the end. Slope intercept form is y=mx + b In this problem we know the new slope, we know an x value and a y value (from the point it passes through), we just don't know the y-intercept (b)

So plugging in 8 for y, -2 for x, and 1/3 for m you get the equation 8 = 1/3*-2 + b

Simplify by multiplying 1/3*-2

8= -2/3 + b

Add 2/3 on both sides (you can use a calculator or remember your fraction addition rules.

24/3 + 2/3 = 26/3

26/3= b We now know m and we know b so we can plug those two values into y=mx + b and get your equation, y= 1/3x + 26/3

Both ways (the way Doug showed and the way I showed) take about the same amount of time, I was just always able to understand this way better.

Answer 2

Since you did not supply the choices--here is how you would determine.

A line perpendicular to the given line will have a slope that is the negative (opposite) reciprocal. Since the given line has a slope of -3, the perpendicular will have a slope of 1/3.

Use point-slope to find the equation:

y - 8 = 1/3 (x - (-2))

y - 8 = 1/3 (x+2)

y = 1/3 x + 2/3 + 8

y = 1/3 x +26/3

See

desmos.com/calculator/zxsfob7lnd

to confirm.