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 use the two points (-7.5, 12) and (3.5, -21).
First, calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (-21 - 12) / (3.5 - (-7.5))
m = -33 / 11
m = -3
Next, choose one of the points to substitute into the slope-intercept form of the linear function (y = mx + b) to solve for the y-intercept (b). Let's choose (-7.5, 12):
12 = -3(-7.5) + b
12 = 22.5 + b
b = 12 - 22.5
b = -10.5
Therefore, the equation of the linear function is:
y = -3x - 10.5