What is an equation of the line that passes through the point ( − 6 , − 7 ) (−6,−7) and is perpendicular to the line 6 x + 5 y = 30 6x+5y=30?

Answer 1

Hi Kayla,

Let's start by writing 6x + 5y = 30 into a form we are familiar with, y = mx + b, where m is the slope and b is the y intercept.

5y = -6x + 30

y = (-6/5)x + 6

Now, we know that the slope of our original line is m = -6/5. To find the slope of the perpendicular line, we can take the negative reciprocal of the original line, which would be a new slope of 5/6.

Now we have the slope of the new line m = 5/6 and a point it passes through (-6, -7).

We can use y = mx + b again by plugging in our known values (x, y, m) to solve for b.

-7 = 5/6*(-6) + b

-7 = -5 + b

b = -2

So the equation of our new line is now

y = (5/6)x - 2