Question

there is no graph for this. Select the coordinates of two points on the line y = -2
A. (2, -2) and (-2, 2)
B. (-2,-2) and (-2, 0)
C. (2, -2) and (0, -2)
D. (2, -2) and (-2, -2)

Answer 1

So it doesn't matter what x-coordinates are chosen, the y-coordinate will always be -2. So any point with y-coordinate of -2 will be on that line.

Answer 2

yes. this question did not have a graph so.......

Answer 3

You don't need one. Any point with a y-coordinate of -2 is one the line y=-2. Choose an answer where the y-coordinates are -2.

Answer 4

it's either b or d?

Answer 5

b has one point with y-coordinate -2 and another point with y-coordinate 0. So it can't be the correct answer.

Answer 6

ok

Answer 7

what about d?

Answer 8

Are both y-coordinates -2?

Answer 9

yes

Answer 10

Great. So those two points must be on the line y=-2. But check the given answers very carefully. The way it is typed above, there are two correct answers. Are you sure you typed it correctly?

Answer 11

nope. for d its ( -2, 2). i switched the numbers

Answer 12

OK. Look for the answer that has y-coordinates of -2. That's the correct one.

Answer 13

C? or D? i cant choose :(

Answer 14

Check D very carefully. You just said you made a mistake typing it in. Are both y-coordinates -2?

Answer 15

yes? these kinds of questions stress me out

Answer 16

No need to stress. Answer D, as you typed it, is (2, -2) and (-2, -2). Then you said you switched the numbers and D should be (-2, 2) and (-2, -2). Am I correct?

Answer 17

yes :)

Answer 18

yes

Answer 19

Sorry. made a mistake myself. If answer D is (-2, 2) and (-2, -2) can it be the solution?

Answer 20

i am gonna say yes

Answer 21

Look carefully. Are both y-coordinates -2?

Answer 22

by the way you replied i am going to say no

Answer 23

OK. What is the y-coordinate of (-2, 2)?

Answer 24

C

Answer 25

Yes. That's correct. Well done.

Answer 26

yay!!!!!

Answer 27

thank you

Answer 28

You're welcome.

Answer 29

write the equation that is perpendicular to the line y = 3/2x + 4 and passes through point (-6, 3)

A. y = 3/2x - 1

B. y = 3/2x + 3

C. y = -2/3x - 1

D. y = -2/3x + 3

Can you help?

Answer 30

^ @ospreytriple can you help?

Answer 31

Well, one characteristic of perpendicular lines is that their slopes are negative reciprocals of each other. What is the slope of the given line?

Answer 32

i looked at the question and it didn't have a slope

Answer 33

Sure it does, we just have to find it. The equation of the given line is y=3/2 x + 4. Recall that the general form of a linear function is y=mx+b, where m is the slope and b is the y-intercept. So what is the slope of y = 3/2 x + 4?

Answer 34

ummmmmmmmmmmmmmmmmmmmmmm...... i don't know. Sorry :(

Answer 35

The slope (m) is the coefficient of x, i.e. the number that is multiplying x. What number is multiplying x in y = 3/2 x + 4 ?

Answer 36

1? i am not good in math.

Answer 37

That's OK. What number is directly in front of the x ?

Answer 38

2?

Answer 39

I guess it's the way that it's typed. Let my retype it for you:
\[y=\frac{ 3 }{ 2 }x\]
Now, what number is multiplying the x? Hint; it's a fraction.

Answer 40

the fraction that is already there? math is not my best subject. and i sound stupid

Answer 41

Yes, it's the fraction that's already there.

Answer 42

yes :)

Answer 43

So, in \[y=\frac{ 3 }{ 2 }x+4\] the x is being multiplied by \[\frac{ 3 }{ 2 }\]. You OK so far?

Answer 44

yes

Answer 45

Good. 3/2 is called the coefficient of x, and it is the slope of the graph of this function. Now a line that is perpendicular to this will have a slope that is the negative reciprocal to 3/2. Do you know what that means?

Answer 46

no. can you please explain it?

Answer 47

No problem, it's quite simple. To take the reciprocal of a number means to turn it upside down. For example, the reciprocal of 4/5 is 5/4 and the reciprocal of 3 is 1/3. Get it? In our question we want the reciprocal of 3/2. What would that be?

Answer 48

2/3

Answer 49

Right. Now the word negative means change the number's sign - if it;s positive, make it negative, if it's negative, make it positive. So the negative reciprocal of 2/5 is -5/2 and the negative reciprocal of -5/6 is 6/5. We want the negative reciprocal of 3/2. What is it?

Answer 50

-2/3

Answer 51

Excellent. So now we know that a line that is perpendicular to \[y=\frac{ 3 }{ 2 }x+4\]must have a slope of -2/3. So, it's equation must look like\[y=-\frac{ 2 }{ 3 }+b\]. OK with that?

Answer 52

yes

Answer 53

Sorry.\[y=-\frac{ 2 }{ 3 }x+b\]

Answer 54

OK. To find b, we substitute the values of x and y from the given point, i.e. (-6, 3) and solve for b. Can you do that?

Answer 55

sorta can you explain and i'll solve?

Answer 56

OK. you'll have\[3=\left( -\frac{ 2 }{ 3 } \right)\left( -6 \right)+b\]Can you take it from here?

Answer 57

yes

Answer 58

Great. What do you get for b?

Answer 59

3 if that's wrong then -1

Answer 60

I love that you provided two answers. The correct one is -1. So now you've got the equation as\[y=-\frac{ 2 }{ 3 }x-1\] and you're done.