Is the relationship shown by the data linear? If so , model the data with an equation.

The data is linear.

The equation in slope intercept form is y = (-5/4)x - 53/4

The equation in standard form is 5x+4y = -53

Explanation:

We know the data is linear because each time x increases by 4, the value of y decreases by 5. The slope is m = (change in y)/(change in x) = -5/4

Use m = -5/4 and one row of x,y values (say x = -9 and y = -2 from the first row) to find the value of b

y = mx+b

-2 = (-5/4)(-9) + b

-2 = 45/4 + b

45/4+b = -2

b = -2 - 45/4

b = -8/4 - 45/4

b = (-8 - 45)/4

b = -53/4

Therefore we go from y = mx+b to y = (-5/4)x - 53/4

We can convert to standard form like so

y = (-5/4)x - 53/4

4y = -5x - 53 ... multiply every term by 4

5x+4y = -53 ... add 5x to both sides

To check the answer, plug in x = -9 and you should get y = -2 as a result

y = (-5/4)x - 53/4

y = (-5/4)*(-9) - 53/4

y = 45/4 - 53/4

y = (45-53)/4

y = -8/4

y = -2

We have confirmed the first row of the table. The other rows will be handled the same way.

step-by-step explanation: