Question

Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y=mx+b form.

y x
6 16
15 43

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

First, let's find the slope using the formula:

m = (y2 - y1) / (x2 - x1)

Using the points (x1, y1) = (16, 6) and (x2, y2) = (43, 15):

m = (15 - 6) / (43 - 16) = 9 / 27 = 1/3

Next, let's find the y-intercept (b) by plugging in one of the points into the equation y = mx + b. Let's use the point (x, y) = (16, 6):

6 = (1/3)(16) + b
6 = 16/3 + b
6 - 16/3 = b
18/3 - 16/3 = b
2/3 = b

Therefore, the equation of the linear function is:

y = (1/3)x + 2/3