Question

The table represents some points on the graph of a linear function. Write a function that represents this relationship.

x y
-4 10
-2 7
6 -5

How to find the linear equation in your calculator:



1. Click on the + in your calculator to get a table.

2. Enter the points in the table.

3. Below the table, type in `y_{1}\sim mx_{1}+b`.

4. The `m` is your slope and the `b` is your y-intercept.

5. Type your equation in the box in slope-intercept form (`y=mx+b`).

y = ___

Answer 1

To find the linear equation that represents the relationship between the points given, we can first calculate the slope \( m \) using two of the points. We'll use the points \((-4, 10)\) and \((-2, 7)\).

The formula for the slope \( m \) is:

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

Using the points \((-4, 10)\) and \((-2, 7)\):

- \( x_1 = -4 \), \( y_1 = 10 \)
- \( x_2 = -2 \), \( y_2 = 7 \)

Calculating the slope:

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

Now that we have the slope, we can use the point-slope form of the equation to find the equation of the line. We can use one of the points; let's use \((-4, 10)\):

The point-slope form is:

\[
y - y_1 = m(x - x_1)
\]

Substituting the values:

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

Distributing the slope on the right side:

\[
y - 10 = -\frac{3}{2}x - 6
\]

Now, we can solve for \( y \) by adding \( 10 \) to both sides:

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

Thus, the equation in slope-intercept form is:

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