Question

The table represents some points on the graph of a linear function

x y
-2 -11
2 -17
4 -20
what function represents this relationship

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the equation of the linear function represented by the given points, we need to determine the slope (m) and the y-intercept (b) of the function.

Using the formula for slope, we can find the slope (m) of the function using any two points:

m = (y2 - y1) / (x2 - x1)
m = (-17 - (-11)) / (2 - (-2))
m = (-17 + 11) / (2 + 2)
m = -6 / 4
m = -3/2

Now that we know the slope, we can use the slope-intercept form of the equation of a line: y = mx + b, where m represents the slope and b represents the y-intercept.

Using the given points, we can choose any point (x, y) to find the y-intercept (b). Let's use the point (2, -17):

-17 = (-3/2)(2) + b
-17 = -3 + b
b = -17 + 3
b = -14

Therefore, the equation of the linear function represented by the given points is:
y = (-3/2)x - 14