The table represents some points on the graph of a linear function. Write a function that represents this relationship.
У
-4
10
-2
7
6
-5
To find the function that represents this relationship, we can first find the slope of the line passing through the points (-4, 10) and (6, -5) using the formula:
slope = (y2 - y1)/(x2 - x1)
slope = (-5 - 10)/(6 - (-4))
slope = (-15)/(10)
slope = -1.5
Next, we can choose one of the points and the calculated slope to write the equation of the line in the slope-intercept form (y = mx + b). Let's use the point (-4, 10):
10 = -1.5*(-4) + b
10 = 6 + b
b = 10 - 6
b = 4
Therefore, the function representing this relationship is:
f(x) = -1.5x + 4