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To find the equation of the linear function, we will first calculate the slope using two of the given points:
slope = (change in y) / (change in x) = (-7.5 - (-4.5)) / (-1 - (-2)) = -3 / 1 = -3
Next, we will use the point-slope form of a linear equation to find the equation of the function:
y - y1 = m(x - x1)
Using the point (-2, -4.5):
y - (-4.5) = -3(x - (-2))
y + 4.5 = -3(x + 2)
y + 4.5 = -3x - 6
y = -3x - 10.5
Therefore, the function representing this relationship is:
y = -3x - 10.5