Question

The table and the equation shown each represent a different linear function.

X Y
0 4
2 12
4 20
6 28

(y=7x+4)

Write the difference in the rates of change for these two functions.

Answer 1

The rate of change of a linear function is the slope.

When you write a linear function's equation in the y = mx + b form,
you can read the slope directly off the equation.
It is m.

What is the slope of the second function?

Answer 2

I don't know. I'm behind in math right now and I haven't learned this stuff yet.

Answer 3

Compare the 2 equations m = slope
Y = mx + b
Y l= 7x + 4

So for this equation m = ?

Answer 4

I don't know. This stuff confuses me a lot. And like I said, I'm behind.

Answer 5

What number in the second equation is in the same position as m in the first equation?

Answer 6

7?

Answer 7

Right - that indicates that 7 is the slope of the line (the graph of the equation will be a straight line.)

Answer 8

Okay.

Answer 9

The slope of the graph gives the rate of change of y compared with x.
So if x increase ashes by 1 unit then y increases by 7units. if x increases by 2 then y will increase by 14 and so on.

Answer 10

* ignore the 'ashes'. Lol

Answer 11

Alright. :)

Answer 12

Now the first function is written as a list of values of x and corresponding values of y
You can work out the slope (rate of change) by looking at the relative differences in their values.

Answer 13

Wait, is it 4?

Answer 14

Note that as x goes from 0 to 2 y increases from 4 to 12
For every increase in 2 of x there's an increase in 8 of y
So slope or rate of changes = 8 / 2 which = 4
Do you follow that OK?

Answer 15

Yes. It's 4

Answer 16

Yep. Thank you so much. :)

Answer 17

So now u have the 2 rates of change
Yw