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 need to calculate the slope and y-intercept using two of the points given in the table.
Using the points (-7.5, 12) and (3.5, -21):
Slope (m) = (change in y) / (change in x) = (-21 - 12) / (3.5 - (-7.5)) = -33 / 11 = -3
Now, use one of the points to find the y-intercept:
Using the point (3.5, -21) and the slope -3, plug into the equation y = mx + b:
-21 = -3(3.5) + b
-21 = -10.5 + b
b = -21 + 10.5
b = -10.5
Therefore, the linear function representing this relationship is:
y = -3x - 10.5