The table represents some points on the graph of a linear function. Write a function that represents this relationship.
x:−4 ,−2, 6
y:10,7, ,−5
To find the linear function that represents this relationship, we can first find the slope by using the formula:
m = (y2 - y1) / (x2 - x1)
Choosing two sets of points:
(−4, 10) and (−2, 7):
m1 = (7 - 10) / (-2 - (-4)) = -3 / 2 = -1.5
Next, choosing another set of points:
(−2, 7) and (6, -5):
m2 = (-5 - 7) / (6 - (-2)) = -12 / 8 = -1.5
Since both calculations resulted in the same slope, we can be confident that the function is linear. We can take one of the points and use the point-slope formula to determine the final linear function:
Using the point (−4, 10):
y - 10 = -1.5(x + 4)
y - 10 = -1.5x - 6
y = -1.5x + 4
Therefore, the function that represents this relationship is:
f(x) = -1.5x + 4