What equation does Landon get if he found the equation of the line passing through the points (2,1) that is perpendicular to the line with equation y=3x+4

Answer 1

Hi Karissa.

I'm going to assume that Landon gets the right answer because he's got me helping him.

There are a few ways to approach this problem, but let's get the easy part out of the way first.

The line we're trying to describe is perpendicular to a line whose slope is 3.

Remember when two lines are perpendicular, the slope of one is the negative reciprocal of the other.

Therefore, the slope of OUR line is -1/3.

Since the question didn't specify what form, our answer should be in, I'm going with everyone's favorite, the slope-intercept form. y = mx + b.

We have our slope, m = -1/3. Since the line passes through the point (2, 1) know that when x = 2, y = 1.

In other words, we HAVE VALUES for x, y and m!

If we plug these values into the form, we get; 1 = -1/3(2) + b.

The ONLY thing we DON'T know is b, but now we can solve for it.

1 = -2/3 + b

1 + 2/3 = b

5/3 = b

The equation for our line is; y = -1/3x + 5/3

I hope this helps.

Answer 2

So first you are going to find the slope of the equation given: 3

This will help you determine the slope of the line that is perpendicular to it. To find the perpendicular slope you need to find the reciproca l- change the sign and flip the fraction: -1/3

Plug the new slope in as m in the y=mx+b formula: y=-1/3x + b

Then using the coordinates given (2,1) you plug it into the the equation to find b: 1=-1/3(2)+b

Solve for b: 5/3

now that you have the slope and the b value your new equation is : y = -1/3x + 5/3