Question

@kirbykirby The graph plots four equations, A, B, C, and D:

Line A joins ordered pair negative 6, 16 and 9, negative 4. Line B joins ordered pair negative 2, 20 and 8, 0. Line C joins ordered pair negative 7, negative 6 and 6, 20. Line D joins ordered pair 7, 20 and 0, negative 7.

Which pair of equations has (4, 8) as its solution?

Equation A and Equation C

Equation B and Equation C

Equation C and Equation D

Equation B and Equation D

Answer 1

@phi @inkyvoyd Please Help!

Answer 2

find the equation of the lines : that is, you can find the line in the form y=mx+b easily by finding the slope "m" first... the slope formula being \[\frac{y_2-y_1}{x_2-x_1}\] where the numerator values are the y-coordinates of your points, and the denominator are the x-coordinates of your points.

Once you have "m" you just need to find the y-intercept "b" which you can do by plugging in either of your 2 points into the formula y = mx+b and then solve for "b"

You should do this for all the lines A, B, C, D

Finally, Just plug in the values of x and y into the line equation for the point (4, 8). If the equation is satisfied (i.e. you get something like "8 = 8") then the point will be on the line . You'll have to try plugging in (4, 8) into all equations and see if the point satisfies the equation

Answer 3

For A I got -20 over 3. For B, -2. For C, 2. And for D, 27 over 7

Answer 4

That are the slopes. I am confused on what to do next?

Answer 5

Or well, actually HOW to do it. I know I need to find the Y-intercept but I am having difficulties doing so.

Answer 6

Once you have the slopes, say for A you got -20/3, then you have this as your equation so far:
\[y = \frac{-20}{3}x+b \]
So you can pick one point (either one of the two is okay), and plug the x and y-coordinates where you see "x" and "y" into the equation, this will allow you to find the y-intercept "b"

Answer 7

So, \[16=\frac{ -20 }{ 3 }(6)+b\]

Answer 8

that 6 should be " - 6"

Answer 9

Oh okay. So instead it would be\[16=\frac{ -20 }{ 3 }(-6)+b\]

Answer 10

But now that I have the equation for A, what is my next step. How do I find the value of B?

Answer 11

Not line B but the (+b) in the equation

Answer 12

You can solve for it algebraically..
\[16 = \frac{-20}{3}(-6)+b\\
16 = \frac{120}{3}+b \]... can you find b? (find the value of 120/3 = ?, and subtract both sides by that value and you will have isolated "b")

Answer 13

-24?

Answer 14

yup!

Answer 15

And B would be:\[20=-2(-2)+b\]

Answer 16

yes

Answer 17

\[16=4+b\]

Answer 18

b=12?

Answer 19

The last step you just have to verify if (4,8) satisfies the equations, so like
8 = m(4) + b

so you need to check if your right side of the equation will equal 8 :)

Answer 20

yes

Answer 21

I hope this gives you enough to finish the exercise as I have to go :o!

Answer 22

It does! Thank You!

Answer 23

yw :) ! byee