To write the equation in slope-intercept form \( y = mx + b \), we first need to determine the slope \( m \) and the y-intercept \( b \).
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Calculate the slope \( m \): The slope \( m \) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
We can use any two points from the table. Let's use the points (2, 11) and (4, 19).
- \( (x_1, y_1) = (2, 11) \)
- \( (x_2, y_2) = (4, 19) \)
Substitute into the slope formula: \[ m = \frac{19 - 11}{4 - 2} = \frac{8}{2} = 4 \]
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Find the y-intercept \( b \): We can use one of the points to find \( b \). Using the point (2, 11) and knowing \( m = 4 \): \[ y = mx + b \] Substitute the known values: \[ 11 = 4(2) + b \] Simplify: \[ 11 = 8 + b \] Solving for \( b \): \[ b = 11 - 8 = 3 \]
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Write the equation in slope-intercept form: Now that we have \( m = 4 \) and \( b = 3 \), the equation is: \[ y = 4x + 3 \]
So, the equation from the given table is: \[ y = 4x + 3 \]