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

$m=\dfrac{y_2-y_1}{x_2-x_1}$

For example, the first two points have a slope of

$m=\dfrac{5-(-3)}{4-2}=\dfrac{8}{2}=4$

The first and third point have a slope of

$m=\dfrac{13-(-3)}{6-2}=\dfrac{16}{4}=4$

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

Answer:

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.

Step-by-step explanation: