Question

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= 9.75, -0.25, -6.5, -14, -17.75

Answer 1

[AI-generated answer — Bot GPT 3.5]

The points on the table represent five coordinates: (-7.5, 9.75), (-3.5, -0.25), (-1, -6.5), (2, -14), and (3.5, -17.75).

To write the linear function that represents this relationship, we need to first calculate the slope (m) using two of the points. Let's use the points (-7.5, 9.75) and (3.5, -17.75) to find the slope:

m = (y2 - y1) / (x2 - x1)
m = (-17.75 - 9.75) / (3.5 - (-7.5))
m = -27.5 / 11
m = -2.5

Now that we have the slope, we can use the point-slope form of the linear equation to write the function:

y - y1 = m(x - x1)

Using the point (-7.5, 9.75):

y - 9.75 = -2.5(x + 7.5)
y - 9.75 = -2.5x - 18.75
y = -2.5x - 9

Therefore, the linear function that represents this relationship is:
y = -2.5x - 9