Answer: y = 5184x
Explanation:
Yes, there is a relationship because, logically, there should be a set amount of pixels changing when the area changes. This data table shows a linear relationship between the square inches of the screen and the number of pixels. To create a linear equation, we need to know the parent function for linear equations: y=mx + b, where "m = rate of change" and "b = initial value or y-intercept"
To find the rate of change (i.e., the slope). To find the rate of change of a linear function, use the formula (y2-y1)/(x2-x1). This formula works because it's essentially using the "rise/run" method of finding the rate of change.
Using the rate of change formula:
(373248-31104) / (72-6) = 5184
We know the rate of change is 5184, and now we simply have to find the "b" value, which is the y-intercept. We do this by plugging in values we know into the y=mx + b equation.
m = 5184, and we can use any set of points in the table for "x" and "y"
31104 = 5184(6) + b
Now, we isolate "b":
31104 - 5184(6) = b
0 = b
The y-intercept ("b" value) is zero, so we can now plug that into our equation:
y = 5184x + 0
y = 5184x