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