Question

Help please....


The table and the graph (attached) each show a different relationship between the same two variables, x and y:

How much more would the value of y be in the table than its value on the graph when x = 11?

A. 100
B. 165
C. 395
D. 440

Answer 1

@inowalst

Answer 2

@TheSmartOne Can you help?

Answer 3

We can start off by finding the equations of the 2 lines.

Answer 4

Okay

Answer 5

So lets start with the table.

We have to chose 2 points. And we can put them in slope-intercept format which is \(\sf y=mx+b\)

Answer 6

So after choosing 2 points (doesn't make a difference which 2) we first calculate the slope.

The slope formula is

\(\Large\sf\frac{y_2-y_1}{x_2-x_1}\)

Answer 7

Wait I'm confused, sorry

Answer 8

Well you see, they want us to find the difference of the y-value when both equations have x=11

But clearly the table stops after 6 and the graph stops after 8. So we are trying to find the equations of both of those lines and then plug in x=11 and then calculate the difference for y.

Answer 9

Ohh

Answer 10

So we can chose 2 points like \(\sf (3,210), (4,280)\)
and use the slope formula to calculate the slope

Answer 11

Okay, can you explain the slope formula you posted earlier?The fraction lookin one

Answer 12

Sure :)

Answer 13

The Slope formula is

\(\Huge\sf\frac{y_2-y_1}{x_2-x_1}\)

I assume you are confused with these 1 and 2's lol :P

But we have two points, remember? Those are in the format of \(\sf (x_1,y_1), (x_2,y_2)\)

Answer 14

Yeah it was the number lol but now it makes sense

Answer 15

So now I put two points from the table in the place of y and x?

Answer 16

yup any 2 points so lets just use
\(\sf (3,210), (4,280)\)
and that would be
\(\sf(x_1,y_1),(x_2,y_2)\)

Soooo
\(\sf x_1 =3\\
y_1 = 210\\ x_2=4 \\ y_2=280\)

Answer 17

\[\frac{ 280- 210}{4-3 }\]

Thats what it would look like?

Answer 18

@TheSmartOne

Answer 19

Sorry I went offline :/

But yes! And when you solve that you get \(\sf\Large\frac{70}{1}=70\)

So we can fill out half of the equation

y=70x+b

Now we plug in a point and solve for b.
(3,210) is the point we will use.
(x,y)
so

\(\sf 210=70\times 3+b\)
\(\sf 270=270+b\)

so b=0

And so our equation is
\(\sf y=70x\)

Answer 20

Its kay and yeah I figured that out XP

Answer 21

And now we do it for the second equation, finding the slope and then the value for b.

We then will plug in x=1 and solve for y and find the difference of the 2 values.

Answer 22

Sorry about ditching you :/

My mom kicked me off the computer and wouldn't let me come back on... So I couldn't even tag someone else to help you through the rest of it.

Answer 23

Nah thats fine :)