Question

The table represents some points on the graph of a linear function.

x y
-4 10
-2 7
6 -5

Create an equation that could represent the relationship.

Move the correct answer to each box. Not all answers will be used.

y = +

Answer 1

To find the equation of a linear function that represents the relationship between \( x \) and \( y \), we need to determine the slope \( m \) and the y-intercept \( b \) of the linear equation in the form:

\[ y = mx + b \]

### Step 1: Calculate the Slope (m)

We can find the slope \( m \) using any two points from the table. Let's use the points (-4, 10) and (-2, 7):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 10}{-2 - (-4)} = \frac{-3}{2} = -\frac{3}{2}
\]

### Step 2: Calculate the Y-Intercept (b)

Now that we have the slope, we can use one of the points to find the y-intercept \( b \). Using the point (-4, 10):

\[
y = mx + b
\]
\[
10 = -\frac{3}{2}(-4) + b
\]
\[
10 = 6 + b
\]
\[
b = 10 - 6 = 4
\]

### Step 3: Write the Equation

Now we can put the values of \( m \) and \( b \) together:

\[
y = -\frac{3}{2}x + 4
\]

### Final Equation

So, the equation that could represent the relationship between \( x \) and \( y \) is:

\[
y = -\frac{3}{2}x + 4
\]

### Filling in the Boxes

If you have specific options to choose from for \( m \) and \( b \), you can fill them in based on this equation:

- For the slope (m), it will be \(-\frac{3}{2}\)
- For the y-intercept (b), it will be \(4\)

Thus, the final answer should be arranged as:

**y = -\frac{3}{2} x + 4**