To write the equation of a line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can use the given slope and the point through which the line passes.
Given:
- Slope \( m = \frac{1}{2} \)
- Point \( (6, 7) \)
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Start with the slope-intercept form of the equation: \[ y = mx + b \]
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Substitute the slope \( m \): \[ y = \frac{1}{2}x + b \]
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Use the point \( (6, 7) \) to find \( b \): Substitute \( x = 6 \) and \( y = 7 \) into the equation: \[ 7 = \frac{1}{2}(6) + b \] Calculate \( \frac{1}{2}(6) \): \[ 7 = 3 + b \] Now, solve for \( b \): \[ b = 7 - 3 = 4 \]
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Now we can write the equation of the line: \[ y = \frac{1}{2}x + 4 \]
Thus, the equation of the line in slope-intercept form is: \[ y = \frac{1}{2}x + 4 \]