Which equation represents a line which is perpendicular to the line y = 5/6x + 8? Explain your choice using words. 1)6x - 5y =-10 2) 6x + 5y = -35 3)06y - 5x = 30 2) 6x + 5y = -35 4) 5x +6y = -18 help

Question

Explain your choice using words. You must also show your work that leads to your answer

Answer 1

Hi, take a look below.

The first equation y = 5/6x + 8 tells us that the slope of this line is m=5/6.

Perpendicular slope is the opposite sign, and reciprocal value. So if m = 5/6, then the perpendicular slope is -6/5. Simply make 5/6 negative and then switch the 5 and 6 as a reciprocal.

Now, which line out of your options has a slope of -6/5? You will need to solve each equation for y and see if m = -6/5 in the form of y = mx + b.

Equation 1: 6x - 5y = -10

-5y = -6x -10

y = 6/5x +2 <----- divide -6 by -5 and you get a positive slope. No good.

Equation 2: 6x + 5y = -35

5y = -6x - 35

y = -6/5x - 7 <----- BINGO!

For the purposes of this response, the answer is shown to be number 2. You should practice the skill by converting all equations into y=mx+b.

Answer 2

y = 5/6x + 8

Slope of the above equation is 5/6

The line that is perpenticular to the above equation has opposite reciprocal slope m = -6/5

Slope intercept form y = -6/5 x + b

Change to standard form 6x + 5y = 5b

b is still unknown but there's only one answer that matches the left side of the equation 6x + 5y

2) 6x + 5y = -35