Question

Side AB of rectangle ABCD is contained within the line y = 2x - 7. What is the slope of the adjacent side, BC?

Answer 1

What property do adjacent sides of a rectangle have?

Answer 2

I dont know what you mean by that?

Answer 3

At what angle do the adjacent sides meet at?

Answer 4

a 90 degree angle?

Answer 5

Good. Now what do you know about the slope of lines which meet at a \(90^{\circ}\) angle?

Answer 6

that its 2x

Answer 7

If two lines are perpendicular, then their slopes will multiply to \(-1\). So for example, \(y=3x+1\) and \(y=-\frac{1}{3}-7\) are perpendicular because \((3)\left(-\frac{1}{3}\right)=-1\).

Answer 8

so the slope is -1/2?

Answer 9

\(y=-\frac{1}{3}x-7\)*

Answer 10

Exactly. Excellent.

Answer 11

Thanks.
can you help me with another question. this one is parallel lines

Answer 12

Sure.

Answer 13

Which of the following is the equation of a line parallel to
4y = 12x + 5 that passes through (3,7)?

Answer 14

Do you prefer point-slope form, for example \(y-3=15(x-4)\), or slope-intercept form, for example \(y=13x+2\)?

Answer 15

The first thing to do, either way, is to figure out the slope of the line they gave you and then think about how the slopes of two parallel lines are related.

Answer 16

If i divide each side by 4 will i end up like this y=3x+5 but i know that isn't correct.

Answer 17

Actually, you will have \(y = 3x + \frac{5}{4}\), which has a slop of what?

Answer 18

3

Answer 19

Now what slope will a parallel line have?

Answer 20

3

Answer 21

Good, and we know it must pass through \((3, 7)\), so we can form a line from this information. Do you know how?

Answer 22

no

Answer 23

Okay, we know that the line has to have the from \(y = mx + b\) and we know \(m=3\). We also know that \((3,7)\) has to be on the line, so it must be a solution to \(y = 3x+b\), whatever \(b\) is (we don't know yet). So we put \((3,7)\) into the equation of our line and solve for \(b\).

Answer 24

so 7=9 + b?

Answer 25

Right. So what is \(b\)?

Answer 26

-2

Answer 27

Good. So what is the final equation?

Answer 28

y=3x-2?

Answer 29

Yup. :)

Answer 30

Thanks so much!

Answer 31

You're very welcome.