Question

Consider the line y=5/3x-7

Find the equation of the line that is parallel to this line and passes through the point (3,5) .

Find the equation of the line that is perpendicular to this line and passes through the point (3,5)

Answer 1

Parallel lines have the same slopes.
So the slope of the parallel line would be 5/3.
Now, because we have the slope and a point on the line, we can use the point-slope format. Do you remember that one?

Answer 2

@Nory um y2-y1/x2-x1 right

Answer 3

That is one form of it. Can you put the slope and the point into that equation to get the equation?

Answer 4

I can put the points but I don't know about the slope @Nory

Answer 5

@Nory wait is it y=5/3+5?

Answer 6

Almost. I believe that it would be y = 5/3x.
Because we have the point (3,5) and 5 = 5/3 * 3.

Answer 7

oh okay @Nory so y=5/3x+5 is my answer for the first question?

Answer 8

I think it would be y = 5/3x...where did you get the 5 from?

Answer 9

(3,5) I took the 5 as the y intercept

Answer 10

Five is not the y-intercept.

Answer 11

So then how would I get it? @Nory

Answer 12

@Nory

Answer 13

Do you know the equation y - y1 = m(x - x1) ?

Answer 14

yes @Nory

Answer 15

Well use that. Use (3,5) for your (x1, y1) and 5/3 for your m.

Answer 16

I get y=5/3x+0 @Nory

Answer 17

Good job! And there's your answer.

Answer 18

I even keep the +0? @Nory

Answer 19

and also that's for the first question?

Answer 20

Now you know how to do the second one, almost. Except that perpendicular lines have opposite reciprocal slopes.
So if the original line has a slope of 5/3, the perpendicular has a slope of -3/5.

Answer 21

Yes it is. You can keep the 0 or not; most people don't require that you keep the 0 on.

Answer 22

Okay! Thank you for the help! @Nory

Answer 23

No problem. Anytime.