To write an equation in slope-intercept form \( y = mx + b \) from the data provided in the table, we first need to determine the slope (\( m \)) and the y-intercept (\( b \)) from the points given.
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From the table, we have the following points:
- (3, -2)
- (6, -3)
- (9, -4)
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Calculate the slope (\( m \)) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] We can use any two points. Let's use (3, -2) and (6, -3): \[ m = \frac{-3 - (-2)}{6 - 3} = \frac{-3 + 2}{3} = \frac{-1}{3} \]
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Now, we can use one of the points (let's use (3, -2)) to find the y-intercept (\( b \)): \[ y = mx + b \Rightarrow -2 = \left(-\frac{1}{3}\right)(3) + b \] \[ -2 = -1 + b \] \[ b = -2 + 1 = -1 \]
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Now that we have both \( m \) and \( b \), we can write the equation in slope-intercept form: \[ y = -\frac{1}{3}x - 1 \]
So, the equation from slope-intercept form that corresponds to the given table is: \[ y = -\frac{1}{3}x - 1 \]