Question

Use the table to answer the 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

Answer 1

To find the equation of the linear function in the form \( y = mx + b \), we need to calculate the slope \( m \) using the given points from the table: \( (6, 16) \) and \( (15, 43) \).

1. **Calculate the slope \( m \)**:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \( (x_1, y_1) = (6, 16) \) and \( (x_2, y_2) = (15, 43) \):

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

2. **Use the slope-point form to find the y-intercept \( b \)**:

We can use one of the points to solve for \( b \). Let's use the point \( (6, 16) \).

\[
y = mx + b
\]
\[
16 = 3(6) + b
\]
\[
16 = 18 + b
\]
\[
b = 16 - 18 = -2
\]

3. **Write the equation in slope-intercept form**:

Now that we have \( m = 3 \) and \( b = -2 \), we can write the equation of the linear function:

\[
y = 3x - 2
\]

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

\[
\boxed{y = 3x - 2}
\]