The table represents some points on the graph of a linear function.
X Y
-2 -11
2 -17
4 -20
Which function represents this relationship?
To find the function that represents this relationship, we need to find the slope and y-intercept of the linear function.
First, let's find the slope (m) using the formula:
m = (change in y) / (change in x)
Using the given points (-2, -11) and (2, -17):
m = (-17 - (-11)) / (2 - (-2))
m = (-17 + 11) / (2 + 2)
m = -6 / 4
m = -3/2
The slope of the linear function is -3/2.
Next, let's find the y-intercept (b). We can choose any point on the line to substitute into the equation to solve for b. Let's use the point (2, -17):
-17 = (-3/2)(2) + b
-17 = -3 + b
b = -17 + 3
b = -14
So the y-intercept of the linear function is -14.
Putting the slope and y-intercept together, the function that represents this relationship is:
y = (-3/2)x - 14