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Write the linear equation \( 2 x-7 y=42 \) in slope-intercept form. .

Ask by Mills Reese. in the United States
Jan 23,2025

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The linear equation \( 2x - 7y = 42 \) in slope-intercept form is \( y = \frac{2}{7}x - 6 \).

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To convert the linear equation \( 2x - 7y = 42 \) into slope-intercept form (\( y = mx + b \)), we first isolate \( y \). Start by moving \( 2x \) to the right side: \[ -7y = -2x + 42 \] Next, divide all terms by \(-7\): \[ y = \frac{2}{7}x - 6 \] Now we have the equation in slope-intercept form, where the slope \( m \) is \( \frac{2}{7} \) and the y-intercept \( b \) is \( -6 \). This shows how the line rises 2 units for every 7 units it runs to the right!

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