I can't seem to get this

Question

I need to find the equation of a line perpendicular to 3y=x-4, passing through (2,2) on a graph? Help?

Answer 1

When you hear "perpendicular" in the context of linear equations, hopefully you recall that the SLOPES perpendicular lines have a special relationship: "opposite reciprocals." That is, take one slope, turn it upside down (reciprocal) and make it the opposite sign (positive / negative), and voila, you have the perpendicular slope.

In the equation you provide, we do not yet know the slope because the slope is the number next to x (COEFFICIENT) only once y is "by itself." So we don't want 3 times y, we want just y, and we must divide each TERM by 3 to easily identify the slope of the equation given:

3y = x - 4 ---> y = 1/3 x - 4/3 (remember, x = 1x, so we divide 1 by 3)

Here, we can see that the slope of the given line is 1/3... so the slope of the line we're being asked to find is -3/1, or simply -3.

Now we can say that the equation we're looking for looks like this, using y = mx + b format:

y = 3x + b (where b is the y-intercept)

We need a number in for b in our final equation, so we take the other information given... (2, 2) means we substitute a 2 in for x and also for y, allowing us to solve for b:

2 = -3(2) + b substitute

2 = -6 + b multiply before you add...

8 = b add 6

Thus, our final equation is this:

y = -3x + 8 :)

Answer 2

Hi, Jocasta,

David has provided the correct answer. I put a file on Google Drive with the graphs.

https://drive.google.com/file/d/1NNmLc-vC6q6x7nOUovx3c_NLlPXWCvUJ/view?usp=sharing

Bob

Answer 3

3y = x - 4 Divide both sides by 3 to get

y = (1/3)x - (4/3)

The slope of the perpendicular line will be the negative reciprocal of the initial line

m= 1/3 for the given line, so for the perpindicular line will have m = -3/1 or just m = -3

We also were given a point on the perpendicular line, (2,2)

We can use point-slope form to find the equation y - y₁ = m * (x - x₁)

y - 2 = -3 (x - 2) We can leave it like this or rearrange to y=mx+b form

y = -3x + 6 + 2

y = -3x + 8 <=This is the equation of the perpendicular line passing through (2,2)