Question

Question #24cfb

Answer 1

`m=-1/2`

Explanation:

The average rate of change, or the slope, of two given points is: `(y_2-y_1)/(x_2-x_1)` (You may not see the significance of `y_2` coming before `y_1`, and `x_2` before `x_1`, but it will matter when you start to work with things like vectors.)

Let's say that `(2,5)` is our first point and `(6,3)` is the second.

Therefore,
`x_1=2,x_2=6,y_1=5,y_2=3`

We have:
`m=(3-5)/(6-2)`
`m=(-2)/4`
`m=-1/2`

That is our answer!

Answer 2

`-1/2`

Explanation:

Rate of change is the the amount of up or down for a given amount of along reading left to right on the x-axis. This is the value of `m` in the standardised form of: `y=mx+x`. Which is the equation of a straight line graph.

This rate of change is called the gradient. Some people call it the slop

`m=("change in "y)/("change in "x) larr" reading left to right"`

Set point 1 as `P_1->(x_1,y_1)=(2,5)`
Set point 2 as `P_2->(x_2,y_2)=(6,3)`

as the first `x` is 2 then we read from `P_1" to "P_2`

`m=("change in "y)/("change in "x) ->P_2-P_1`

`m=("change in "y)/("change in "x)=(y_2-y_1)/(x_2-x_1)=(3-5)/(6-2)=(-2)/(+4)=-1/2`

As the gradient is negative it means the 'slope' is downward as you read left to right.