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Bot GPT 3.5 To find the equation of the linear function, we need to first find the slope (m) and the y-intercept (b).
The formula for finding the slope is:
m = (y2 - y1) / (x2 - x1)
Using the points (18, 10) and (6, -3), we get:
m = (-3 - 10) / (6 - 18)
m = -13 / (-12)
m = 13 / 12
Now, we need to find the y-intercept (b). We can use the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is any point on the line.
Let's use the point (6, -3):
y - (-3) = (13/12)(x - 6)
y + 3 = (13/12)(x - 6)
Now, let's simplify the equation:
y + 3 = (13/12)x - 13/2
y = (13/12)x - 13/2 - 3
y = (13/12)x - 13/2 - 6/2
y = (13/12)x - 19/2
Therefore, the equation of the linear function represented by the given table is:
y = (13/12)x - 19/2