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
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Step-by-step 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
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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.