Question

Need answer to 9 and 10 please help!! 40 points

Answer 1

Data can be modeled by a linear equation if all of the points lay on the same line. This happens if every pair of points have the same slope, which we can calculate as

`m=(y_2-y_1)/(x_2-x_1)`

For example, the first two points have a slope of

`m=(5-(-3))/(4-2)=(8)/(2)=4`

The first and third point have a slope of

`m=(13-(-3))/(6-2)=(16)/(4)=4`

You can check that all the other pairs always share a slope of 4. This is enough to claim that the points lay on the same line.

To write the equation of the said line, we can use the following formula: given a point
`(x_0,y_0)` and a slope
`m`, the line passing through that point with that slope has equation

`y-y_0=m(x-x_0)`

Plugging the coordinates of the first point (for example) and the slope we found out, we have

`y-(-3)=4(x-2) \iff y +3= 4x-8 \iff y=4x-11`

Answer 2

The table provided has a proportion of x increases by 2 while y increases by 8. So it would be increasing 8 each time forming a linear graph.

Sorry however I don't know the answer to 10.

Explanation: