Use the table to answer the question.

Question

This table shows the relationship between x and y values that will contribute to linear functions.
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)
y=
x−

Answer 1

To find the equation of the linear function in the form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \).

1. Calculate the slope \( m \): The slope \( m \) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points provided: (6, 16) and (15, 43), we can assign:

   • \( (x_1, y_1) = (6, 16) \)
   • \( (x_2, y_2) = (15, 43) \)

   Plugging these values into the formula: \[ m = \frac{43 - 16}{15 - 6} = \frac{27}{9} = 3 \]

2. Use the slope-intercept form: Now that we have \( m = 3 \), we can use one of the points to find \( b \) (the y-intercept). Let's use the point (6, 16): \[ y = mx + b \] Substituting \( m \) and the point (6, 16): \[ 16 = 3(6) + b \] Simplifying: \[ 16 = 18 + b \] \[ b = 16 - 18 = -2 \]

3. Write the final equation: Now we can write the equation in the form \( y = mx + b \): \[ y = 3x - 2 \]

So, the equation of the linear function is: \[ \boxed{y = 3x - 2} \]