Question

Is the line through points P(3, –5) and Q(1, 4) parallel to the line through points R(–1, 1) and S(3, –3)? Explain.

Choose one answer.
a. Yes; the lines have equal slopes.
b. Yes; the lines are both vertical.
c. No; the lines have unequal slopes.
d. No; one line has zero slope, the other has no slope.

Answer 1

you gotta compute the slope of each
for example, the slope of the first one is
\[\frac{4-(-5)}{1-3}=\frac{9}{-2}\]

Answer 2

if the second one has the same slope then they are parallel
it does not however

Answer 3

you know how to find the slope of the second one?

Answer 4

Not really. I've been trying to figure it out. That's why I haven't replied yet.

Answer 5

it is always
\[\frac{y_2-y_1}{x_2-x_1}\]

Answer 6

for \((-1,1)\) and \((3,-3)\) it would be
\[\frac{-3-1}{3-(-1)}\]

Answer 7

which, if my arithmetic is correct, is just \(-1\)

Answer 8

Alright I'll try and figure it out. And post it and you tell me if it's right!

Answer 9

ok

Answer 10

Is the answer D?

Answer 11

no
D says one line has zero slope, but we calculated the slope of the first one and got
\[-\frac{9}{2}\]

Answer 12

i wrote above how to calculate the slope of the other line
can you see where i wrote that?

Answer 13

Yes.

Answer 14

I'm trying to figure out which one i'm calculating.

Answer 15

you have to calculate both of them to answer this question

Answer 16

i calculated the first one as \(-\frac{9}{2}\)

Answer 17

So for the second would I do.

1 - 3 and 4 - (-5) ?

Answer 18

that is the first one
and no that is not quite right
you want to do the first or the second
you pick we will do it slowly

Answer 19

Either one is fine.

Answer 20

ok lets compute the slope of the line with points \((3,-5)\) and \((1,4)\)

Answer 21

it is always
\[\frac{y_2-y_1}{x_2-x_1}\]
in your example \(y_2=4,y_1=-5, x_2=1,x_1=3\)

Answer 22

when we substitute those numbers in to find the slope, you get \[\frac{4-(-5)}{1-3}\]

Answer 23

after doing the arithmetic, you have a slope of
\[-\frac{9}{2}\]

Answer 24

Okay, I got that finally.

Answer 25

whew now on to the next one?

Answer 26

Yes.

Answer 27

points are \((-1,1)\) and \((3,-3)\)

Answer 28

it is still \[\frac{y_2-y_1}{x_2-x_1}\] but this time
\[y_2=-3,y_1=1,x_2=3,x_1=-1\]
you want to try it?

Answer 29

Yes, please!

Answer 30

go ahead, let me know what you get

Answer 31

-1 is what I got.

Answer 32

you win

Answer 33

Yay! Finally.

Answer 34

that means the final answer is C,
it is C 95% of the time, so we probably could have guessed that from the beginning

Answer 35

I was going to say C earlier, but I wasn't sure.

can you help me with three more please!

Answer 36

sure go ahead we can do them

Answer 37

Thank you!

What is an equation in point-slope form for the line perpendicular to y = 2x + 13 that contains (8, –4)?

A. y + 4 =-1/2(x-8)
B. x + 4 = 2(y – 8)
C.y + 8 =-1/2(x-4)
D.y + 4 = 2(x – 8)

Answer 38

i got a raft of question marks
instead of copy and paste, it would be best to make a screen shot

Answer 39

i could try to refresh my browser maybe that would work

Answer 40

Try and let me know.

Answer 41

that's better

Answer 42

It's been doing it to me, as well. So it might be this website.

Answer 43

perpendicular to \(y=2x+3\)
slope of \(y=2x+3\) perpedicular line will have slope \(-\frac{1}{2}\) the "negative reciprocal

Answer 44

you mean y=2x + 13?

Answer 45

yeah right
makes no difference really

Answer 46

slope is still \(-\frac{1}{2}\) for the perpendicular line

Answer 47

Okay gotcha!

Answer 48

the point is \((8,-4)\) and the slope is \(-\frac{1}{2}\) the point slope formula gives
\[y-(-4)=-\frac{1}{2}(x-8)\] or
\[y+4=-\frac{1}{2}(x-8)\]

Answer 49

So would it be A?

Answer 50

yes, a rare A

Answer 51

Next Question

A. y = 1/3(x) - (-4)
B. y= 1/3(x) + (-2/3)
C. y= 3(x) + (-10/3)
D. 3(x) + (-2/3)

Answer 52

D. y=*

Answer 53

this kind of sucks because i cannot read the two points clearly
one thing is for sure, the slope is not 3, it is \(\frac{1}{3}\)

Answer 54

Do you need me to tell you the two points?

Answer 55

in any case we don't really need to do much more
the slope is \(\frac{1}{3}\) because the line goes right 3 up 1
the y intercept is not \(-4\) is is some negative fraction

Answer 56

from your eyeballs using no computation, you get to pick B

Answer 57

do you see what i mean by the y intercept? where the line crosses the y axis

Answer 58

The points are -4, 2 and 5, 1 and yes i see where your coming from.

Answer 59

-4, -2*

Answer 60

so we need go no further
the y intercept is not -4
pick B

Answer 61

Okay!
Next Question.

Marks: 1
What is the equation in point-slope form for the line parallel to y = –2x + 10 that contains J(6, 8)?
Choose one answer.
a. y – 8 = –2(x – 6)
b. y – 8 = 2(x – 6)
c. y + 8 = –2(x – 6)
d. x – 8 = 2(y – 6)

Answer 62

You might have to Refresh again. It did the question marks.

Answer 63

hold on let me refresh again

Answer 64

ok that's better
parallel
that means they have the same slope
what is the slope of \(y=-2x+10\) ?

Answer 65

-2?

Answer 66

yeah so it is like the other one
\[y-y_1=m(x-x_1)\] with
\[m=-2, x_1=6,y_1=8\]

Answer 67

let me know what you get

Answer 68

A.

Answer 69

ok looks good

Answer 70

Thank you!!

One more thing before I submit my test can you check my answers for the questions I did myself?

Answer 71

sure why not

Answer 72

What is an equation for the line that passes through points (4, –4) and (8, 4)?
Choose one answer.
a. (y + 4) = –2(x – 4)
b. (y – 4) = –2(x + 4)
c. (y – 4) = 2(x + 4)
d. (y + 4) = 2(x – 4)

I choose C.

Answer 73

crap hold on

Answer 74

ok back

Answer 75

did you get this \[y+4 = 2 (x-4)\]

Answer 76

oh no you got the signs backwards

Answer 77

should be D i think

Answer 78

What must be true about the slopes of two perpendicular lines, neither of which is vertical?
Choose one answer.
a. The slopes have product 1.
b. The slopes are equal.
c. The slopes have product –1.
d. One of the slopes must be 0.

I choose C again.

Write an equation in point-slope form of the line through point J(4, –4) with slope 4.

A. y + 4 = 4 (x + 4)
B. y - 4 (x + 4)
C. y + -4 (x -4)
D. y + 4 (x -4)

C again.

Answer 79

Okay I changed it! thank you!

Answer 80

first one
the slopes have a product equal -1
was that the choice C?

Answer 81

I choose C for both.

Answer 82

And yes.

Answer 83

\[y+4=4(x-4)\] is that a choice?

Answer 84

your choices are missing some equal signs, so it is not clear but that is the right answer

Answer 85

C is the right answer or the one you said.
It doesn't have that as the answer.
but it has y + 4 = 4 (x + 4)

Answer 86

hmm hold on

Answer 87

it definitely should be
\[y+4=4(x-4)\]

Answer 88

Alright it has that answer! I'm sorry!

Answer 89

whew

Answer 90

then pick it!

Answer 91

Write an equation in slope-intercept form of the line through points S(–7,–6) and T(10,8).

A. y = -14/17x + 4/17
B. y= -14/17x - -4/17
C. y = 14/17x - 4/17
D. y = 14/17x + 4/17

D is my answer.

Answer 92

Write the equation for the horizontal line that contains point G(3, 4).
Choose one answer.
a. y = 4
b. y = 3
c. x = 3
d. x = 4
Answer: A
Write the equation for the vertical line that contains point E(–7, 7).
Choose one answer.
a. y = –7
b. x = –7
c. y = 7
d. x = 7
Answer: B

Answer 93

once again...

Answer 94

A is right

Answer 95

B is right too

Answer 96

these are the last questions.

Answer 97

that was it?