The table represents some points on the graph of a linear function. Write a function that represents this relationship.
x -7.5, -3.5, -1, 2, 3.5 y 12, 0, -7.5, -16.5, -21
To find the linear function that represents this relationship, we can start by finding the slope of the line passing through two points:
(2, -16.5) and (-1, -7.5)
Slope (m) = (y2 - y1) / (x2 - x1)
m = (-7.5 - (-16.5)) / (-1 - 2)
m = 9 / -3
m = -3
Now that we have the slope, we can use the point-slope form of the equation of a line to find the linear function:
y - y1 = m(x - x1)
Using the point (2, -16.5):
y - (-16.5) = -3(x - 2)
y + 16.5 = -3x + 6
y = -3x - 10.5
Therefore, the linear function representing this relationship is y = -3x - 10.5.