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.
To find the equation of the linear function that models the relationship shown in the table, we need to determine the values of slope (m) and y-intercept (b).
First, we need to find the slope (m) using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the values from the table:
x₁ = 6, y₁ = 16
x₂ = 15, y₂ = 43
We can substitute these values into the formula:
m = (43 - 16) / (15 - 6)
m = 27 / 9
m = 3
Now that we have the slope, we can find the y-intercept (b) by substituting one of the points from the table into the slope-intercept form: y = mx + b.
Using the point (6, 16):
16 = 3(6) + b
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.