Answer:
y -12 = -4.25(x +4)
Explanation:
You want the equation that describes the relation shown in the given table.
Graph
The given x-values are not evenly spaced, and the y-values do not differ by integer values. Hence it seems possible that the required equation is nonlinear.
One way to tell is to find the slopes between adjacent points. Another way to tell is to plot them on a graph. We chose the latter approach, as we have access to a graphing calculator that makes this simple.
It appears the points lie on the same line. (see attached)
Slope
The slope can be found from the first two points:
m = (y2 -y1)/(x2 -x1)
m = (3.5 -12)/(-2 -(-4)) = -8.5/2 = -4.25
Point-slope equation
The point-slope equation of a line has the form ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
Using the first point's coordinates, the equation of the line can be written as ...
y -12 = -4.25(x +4)
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Check
We can check to make sure the last point is on this line:
-26.25 -12 = -4.25(5 +4)
-38.25 = -4.25(9) . . . . . true