Question

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)

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 formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \((6, 16)\) and \((15, 43)\):
- \(x_1 = 6\), \(y_1 = 16\)
- \(x_2 = 15\), \(y_2 = 43\)

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

2. **Use the slope and one of the points to find the y-intercept \(b\):**
We can use the point-slope form \(y = mx + b\). Let's use the point \((6, 16)\):
\[
16 = 3(6) + b
\]
Calculating:
\[
16 = 18 + b
\]
\[
b = 16 - 18 = -2
\]

3. **Write the equation:**
Now that we have both \(m\) and \(b\), 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:
\[
\boxed{y = 3x - 2}
\]