Which equation models the relationship in the table?

Question

Which equation models the relationship in the table?
A table of values is shown:
x | 4 | 7 | 10 | 13
y | -12 | -17 | -22 | -27
○ y + 22 = -\frac{5}{3}(x - 10)
○ y - 22 = -\frac{5}{3}(x + 10)
○ y + 22 = -\frac{3}{5}(x - 10)
○ y - 22 = -\frac{3}{5}(x + 10)

SnapAndSolve AI · Accepted Answer

To find the equation that models the relationship in the table, we need to determine the slope and the y-intercept of the line that fits the data points.

First, calculate the slope (m) using two points from the table, for example, (4, -12) and (7, -17):

m = (y2 - y1) / (x2 - x1) = (-17 - (-12)) / (7 - 4) = -5 / 3

Now, use the point-slope form of the equation y - y1 = m(x - x1) with one of the points, say (10, -22):

y + 22 = -\frac{5}{3}(x - 10)

Therefore, the correct equation is:

y + 22 = -\frac{5}{3}(x - 10)

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Which equation models the relationship in the table?

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