Question

A table of values representing a linear relationship is shown.
x y
-5 3
-1 -1
1 -3
4 6
Which equation models this relationship in slope-intercept form?
y = -7/3x - 2
y = x + 2
y = -x - 4
y = -x - 2

Answer 1

To find the equation that models the linear relationship given the table of values, we can calculate the slope (m) and the y-intercept (b) for the slope-intercept form of a linear equation, which is \(y = mx + b\).

### Step 1: Calculate the slope (m)
The slope \(m\) can be calculated using any two points from the table. We can take points \((-5, 3)\) and \((-1, -1)\).

Using the formula:

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

Substituting the values:

\[
m = \frac{-1 - 3}{-1 - (-5)} = \frac{-4}{4} = -1
\]

### Step 2: Find the y-intercept (b)
Next, we can use one of the points and the slope to find the y-intercept. Using the point \((-1, -1)\):

\[
y = mx + b \implies -1 = -1(-1) + b
\]
\[
-1 = 1 + b \implies b = -1 - 1 = -2
\]

### Step 3: Write the equation
Now that we have \(m = -1\) and \(b = -2\), we can write the equation in slope-intercept form:

\[
y = -1x - 2 \quad \text{or} \quad y = -x - 2
\]

### Conclusion
The equation that models this relationship in slope-intercept form is:

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