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 begin by finding the slope using two points from the table. Let's use the points (-1, -7.5) and (2, -16.5):
slope (m) = (y2 - y1) / (x2 - x1)
m = (-16.5 - (-7.5)) / (2 - (-1))
m = (-16.5 + 7.5) / (2 + 1)
m = -9 / 3
m = -3
Now that we have the slope, we can use the point-slope form to find the equation of the linear function:
y - y1 = m(x - x1)
y - (-7.5) = -3(x - (-1))
y + 7.5 = -3(x + 1)
y + 7.5 = -3x - 3
y = -3x - 3 - 7.5
y = -3x - 10.5
Therefore, the linear function that represents this relationship is y = -3x - 10.5.