Use the table to answer the question.

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)

Answer 1

To find the equation of the linear function that models the relationship shown in the table, we can use the two points provided: (6, 16) and (15, 43).

First, we will calculate the slope (m) using the formula:

$$m=\frac{y_2-y_1}{x_2-x_1}$$

Using our points:

• Point 1: (6, 16) → $x_1=6$, $y_1=16$
• Point 2: (15, 43) → $x_2=15$, $y_2=43$

Substituting these values into the slope formula:

$$m=\frac{43-16}{15-6}=\frac{27}{9}=3$$

Now that we have the slope (m = 3), we can use one of the points to find the y-intercept (b). We will use point (6, 16) with the equation of the line in the form $y=mx+b$:

$$16=3(6)+b$$

Calculating this gives us:

$$16=18+b$$

Now solve for $b$:

$$b=16-18=-2$$

Now that we have both the slope and the y-intercept, we can write the equation of the line:

$$y=3x-2$$

Thus, the equation of the linear function that models the relationship shown in the table is:

$$\boxed{{\displaystyle y=3x-2}}$$