Question

1.Write the equation of a line parallel to the line 2x + 3y = 5 and passes through the point (9, -3)

2. Write the equation of a line in slope-intercept form that has a slope of -2 and passes through the point (2, -8).
A. y = -2x - 4
B. y = -2x - 8
C. y = -2x + 18
D. y = -2x – 12
3. Write an equation of a line in point-slope form that has a slope of -2 and passes through (5, -1).
A. y + 1 = -2(x – 5)
B. y – 1 = -2(x – 5)
C. y – 5 = -2(x + 1)
D. y -5 = -2(x – 1)

Answer 1

1) If you want a parallel line to ax+by=c, it must be of the form, ax+by=n, where you must find the value of n using the point they give you.
Do you understand it?

Answer 2

not really.

Answer 3

For example, a line parallel to the line 2x+3y=5 is, 2x+3y=8. Do you see what they have in common?

Answer 4

yeah the 2x+3y

Answer 5

Perfect, so in your problem the line must be that way: 2x+3y=n, but you don't know the value of n. Ok?

Answer 6

ok

Answer 7

Well, we must use the point the give us and substitute in our equation, so (x,y)=(9,-3), that is, x=9 and y=-3,
\[2x+3y=n\Rightarrow 2\cdot 9+3\cdot (-3)=n\]What value do you obtain for n?

Answer 8

9?

Answer 9

whit nvm lemme do that again

Answer 10

Perfect, so the solution is 2x+3y=9.

Answer 11

oh so it is 9?

Answer 12

Yes, the solution to the first problem is 2x+3y=9. :)

Answer 13

okay(: thanks.
can you help with the other 2 now?

Answer 14

Of course. For the second question you should remember the point-slope form of the line,
\[y=mx+n\]where m is the slope, and n the y intercept. With the data of the problem and the point-slope equation, could you say me what is the correct answer?

Answer 15

would it be c?

Answer 16

-2x+18?

Answer 17

As you see, all lines satisfy the condition: slope=-2. So our equation should be of the form,
\[y=-2x+n\]But we neew to find n. Again you must substitue x and y with the values they give you, x=2 and y=-8 (but it is not c).

Answer 18

Other form to check it is to do x=2 in each solution, and see what of the equations gives you y=-8.

Answer 19

4

Answer 20

with a minus sign, so it should be A, y=-2x-4, because when you do x=2, you obtain y=-8. Ok?

Answer 21

okay so it's A?

Answer 22

Yes, by the reason I gave you.

Answer 23

okay(:
& now can you help me with the last one?

Answer 24

The third problems it should be easier. The point intercept equation has the form,
\[y-y_0=m(x-x_0)\]In the problem says you slope=m=-2, and the point is (x0,y0)=(5,-1). Could you select the correct answer with this data?

Answer 25

my guess would be either C or D

Answer 26

I give you a hint.
\[y-(-1)=-2(x-5)\]:)

Answer 27

a?

Answer 28

Perfect. I hope it helps you (but I think you must rework it a little).