To find the equation of a line in slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), we can use the slope \( m = 6 \) and the point \( (2, 7) \).
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Substitute the values into the slope-intercept form: We know the slope \( m = 6 \), so our equation starts as: \[ y = 6x + b \]
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Use the point to solve for \( b \): Substitute \( x = 2 \) and \( y = 7 \) into the equation: \[ 7 = 6(2) + b \]
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Calculate \( 6(2) \): \[ 6(2) = 12 \] So, we have: \[ 7 = 12 + b \]
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Solve for \( b \): \[ b = 7 - 12 = -5 \]
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Write the final equation: Now that we have \( b = -5 \), the equation of the line is: \[ y = 6x - 5 \]
Thus, the equation of the line in slope-intercept form is: \[ \boxed{y = 6x - 5} \]