Question

Find the average rate of change for the given function from x = - 2 to x = 1.

http://learn.flvs.net/webdav/assessment_images/educator_algebra2_v13/01_00_pretest/01_00_75.gif

-1
1
-3
3

Answer 1

Hey We :)

We don't have access to your flvs account, so we can't see the picture.
Can you type the function out maybe?

Answer 2

Here's the picture

Answer 3

They didn't even squeeze the line onto the graph at x=-2,
that's really annoying.

But anyway, since this is a `linear` function,
it's rate of change will stay the same no matter where we measure it from.

Answer 4

Let's use the points where it intersects the x and y axes.
When x=0, it looks like the line is passing through y=-5, yah?
And then at y=0, our line passes through x=5.

Answer 5

Our slope formula:
\[\Large\rm m=\frac{y_2-y_1}{x_2-x_1}\]
Plugging in our points:
\(\Large\rm (5,0)\quad \text{and}\quad (0,-5)\)
will give you the average rate of change.

Answer 6

do you mean that i have to plug in 5 for y2, 0 for y1 & 0 for x2 & -5 for x1?

Answer 7

\[\Large\rm (\color{orangered}{5},\color{royalblue}{0})\quad \text{and}\quad (\color{orangered}{0},\color{royalblue}{-5})\]Orange are your x's,
Blue are your y's.\[\Large\rm m=\frac{\color{royalblue}{y_2-y_1}}{\color{orangered}{x_2-x_1}}\]

Answer 8

\[\Large\rm m=\frac{\color{royalblue}{0-(-5)}}{\color{orangered}{5-0}}\]

Answer 9

what do i do after this?

Answer 10

Hmm we are `subtracting a negative` on our 5, we can rewrite that as addition.\[\Large\rm m=\frac{0-(-5)}{5-0}\]\[\Large\rm m=\frac{0+5}{5-0}\]\[\Large\rm m=\frac{5}{5}\]Then simplify c:
That will tell you the average rate of change between any two points on the line.

Answer 11

i think the answer is positive 1 because i divided 5 with 5

Answer 12

yay good job \c:/

If we had been able to use the point at x=-2 and x=1,
we would have instead come up with 3/3.
But as you determined, that simplifies to 1.

Answer 13

thank you for the help i really appreciate it. do you mind helping me with another question?

Answer 14

sure

Answer 15

well a couple more questions