Question

What is the relationship between the lines determined by the following two equations?

6x – 2y = 16
y = 3x – 8

parallel
perpendicular
neither parallel nor perpendicular
they are the same line

Answer 1

First, let's take 6x – 2y = 16 and simplify it.
Therefore -2y = -6x + 16
Therefore y = 3x -8
Which is the same as the second equation given.
Therefore the lines are the same.

Answer 2

Can you help me with a few more? c:

Answer 3

Which of the following has a slope of –2 and a y-intercept of 4?

y = –2x + 4
y = 2x + 4
y = 2x – 4
y = –2x – 4

Answer 4

Sure, I can try. ^-^

Answer 5

In the standard equation y = mx + c, the value of m is the slope of the line, and the value of c is the y-intercept.
So, comparing the given equations to this standard form, the slopes and y-intercepts are as follows: -2 and 4, 2 and 4, 2 and -4, -2 and -4. Therefore the first equation is the one we are looking for.

Answer 6

these are of the form: y=mx+c
where m=slope and c=y intercept
now try to do tis on ur own

Answer 7

Ah that makes sense! thank you, I have I think 2 more if you dont mind helping me, I really really appreciate it! @inco

Answer 8

Ok, sure!

Answer 9

The graph of a line has a slope of 3 and passes through the point (–4, –5). What is the equation of the line in point-slope form?

y + 4 = 3(x + 5)
y – 4 = 3(x – 5)
y + 5 = 3(x + 4)
y – 5 = 3(x – 4)

Answer 10

Well, I'm not exactly sure how this one is meant to be solved, but this is how I'd do it:
To find the equation of the line required, we suubstitute m = 3 and (-4, -5) into y = mx +c.
Therefore, -5 = 3(-4) + c
Therefore, -5 = -12 + c
Therefore, c = 7
So the equation of the line equals y = 3x + 7
Now we simply the options given:
y + 4 = 3(x + 5) -> y = 3x + 11
y – 4 = 3(x – 5) -> y = 3x - 11
y + 5 = 3(x + 4) -> y = 3x + 7
y – 5 = 3(x – 4) -> y = 3x - 7

Therefore, the required equation is the third one.

On a side note, the way I just solved it is probably an unnecessarily long way of doing so, but I cannot think of another way right now.

Answer 11

Okay, that makes sense, I'll write this down. Two more then I think I'm done! I really appreciate your time and help.

What are the x- and y-intercepts of the line?

2x – 3y = –12

x-intercept 6, y-intercept –4
x-intercept –6, y-intercept 4
x-intercept –4, y-intercept 6
x-intercept 4, y-intercept –6


Question 12.12. Select the equation of the line that passes through the point (–2, –1) and has slope 5 in point-slope form.

(y – 1) = 5(x – 2)
(x + 2) = 5(y – 1)
(x – 2) = 5(y + 1)
(y + 1) = 5(x + 2)

Answer 12

Right. To find the intercepts of the line 2x – 3y = –12, we proceed as follows.

For the y-intercept, when x = 0, 2(0) - 3y = -12.
Therefore, -3y = -12
Therefore, y = 4

For the x-intercept, when y = 0, 2x - 3(0) = -12
Therefore, 2x = -12
Therefore, x = -6

Therefore the y-intercept is 4, and the x-intercept is -6.

In general, to find the y-intercept, we substitute x = 0 into the equation, and to find the x-intercept, when substitute in y = 0.

Answer 13

Ah! Thank you! c:

Answer 14

I don't quite understand the last one?

Answer 15

For the last one, I think I'm going to solve it like I did that earlier one I wasn't sure about. So here goes:

To find the equation of the line required, we suubstitute m = 5 and (-2, -1) into y = mx +c.
Therefore, -1 = 5(-2) + c
Therefore, -1 = -10 + c
Therefore, c = 9
So the equation of the line equals y = 5x + 9
Now we simply the options given:
(y – 1) = 5(x – 2) -> y - 1 = 5x - 10 -> y = 5x - 9
(x + 2) = 5(y – 1) -> x + 2 = 5y - 5 -> 5y = x + 7 -> y = (1/5)x + 7/5
(x – 2) = 5(y + 1) -> x - 2 = 5y + 5 (This isn't the one either. XD)
(y + 1) = 5(x + 2) -> y + 1 = 5x + 10 -> y = 5x + 9

Therefore, the required equation is the last one.

Answer 16

Ohhh! okay, thank you so much for taking your time to help me c:

Answer 17

You're welcome! :D