Question

I’m the relationship shown by the data linear, if so, model with an equation . A. The relationship is linear;

Answer 1

The relation is data if the difference between every 2 x is equal and the difference between every 2 y is equal

Since:

-5 - (-7) = -5 + 7 = 2

-3 - (-5) = -3 + 5 = 2

-1 - (-3) = -1 + 3 = 2

Since:

9 - 5 = 4

13 - 9 = 4

17 - 13 = 4

Then

The difference between every 2 x is constant and the difference between every 2 y constant

Then the relation is linear

Since the form of the linear equation is

`y-y_1=m(x-x_(1))`

m is the rate of change of y with respect to x (the slope of the line)

(x1, y1) is a point on the line

Let us find m

`\begin{gathered} m=(\Delta y)/(\Delta x) \\ \Delta y=4 \\ \Delta x=2 \\ m=(4)/(2) \\ m=2 \end{gathered}`

Since x1 = -7 and y1 = 5, then

`\begin{gathered} y-5=2(x--7) \\ y-5=2(x+7) \end{gathered}`