Use the table to answer the question.
x y
6 16
15 43
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y=mx+b form.
(1 point)
To find the equation of the linear function, we need to find the slope (m) and the y-intercept (b).
First, let's find the slope:
The slope (m) is the change in y divided by the change in x.
Here, when x changes from 6 to 15, y changes from 16 to 43.
Change in x = 15 - 6 = 9
Change in y = 43 - 16 = 27
So, the slope (m) = 27/9 = 3.
Next, let's find the y-intercept (b):
We can choose any point from the table to find the y-intercept. Let's choose (6, 16).
The equation of a line in slope-intercept form is y = mx + b.
Substituting the values, we have:
16 = 3(6) + b
Simplifying, we get:
16 = 18 + b
b = 16 - 18
b = -2.
Therefore, the equation of the linear function that models the relationship shown in the table is:
y = 3x - 2.