To find the equation that models the linear relationship in slope-intercept form \(y = mx + b\), we first need to calculate the slope (\(m\)) using two points from the table.
Let's use the points \((-2, -7)\) and \((2, 1)\):
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 the points: \[ m = \frac{1 - (-7)}{2 - (-2)} = \frac{1 + 7}{2 + 2} = \frac{8}{4} = 2 \]
Now that we have the slope \(m = 2\), we can use one of the points to find the y-intercept \(b\). Let's use the point \((0, -3)\) because it already has the \(y\) value for \(x = 0\), implying that \(b = -3\).
Thus, the equation of the line in slope-intercept form is: \[ y = 2x - 3 \]
Now let's verify that this equation holds true for the other points in the table.
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For \(x = -2\): \[ y = 2(-2) - 3 = -4 - 3 = -7 \quad \text{(Point is correct)} \]
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For \(x = 2\): \[ y = 2(2) - 3 = 4 - 3 = 1 \quad \text{(Point is correct)} \]
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For \(x = 4\): \[ y = 2(4) - 3 = 8 - 3 = 5 \quad \text{(Point is correct)} \]
Since the equation holds for all points, the correct equation that models this relationship in slope-intercept form is: \[ \boxed{y = 2x - 3} \]
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