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. (1 point) y= x−

Answer 1

To find the equation of the linear function that models the relationship shown in the table, we need to determine the slope (m) and the y-intercept (b).

Given points from the table:
- Point 1: (6, 16)
- Point 2: (15, 43)

### Step 1: Finding the slope (m)

The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Substituting in our points:

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

### Step 2: Finding the y-intercept (b)

Now we can use one of the points to find the y-intercept (b). We'll use the point (6, 16).

The equation of a line in slope-intercept form is:

\[
y = mx + b
\]

Substituting \(m = 3\) and the point (6, 16):

\[
16 = 3(6) + b
\]

This simplifies to:

\[
16 = 18 + b \implies b = 16 - 18 \implies b = -2
\]

### Step 3: Writing the equation

Now we can write the equation of the linear function:

\[
y = 3x - 2
\]

Thus, the final answer is:

\[
y = 3x - 2
\]