1Cademy - Finding the Equation of a Line Parallel to $$y = \frac{1}{2}x

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Finding an Equation of a Line Parallel to a Given Line

Example

Finding the Equation of a Line Parallel to $y = \frac{1}{2}x - 3$ Through $(6, 4)$

To construct the algebraic equation for a line that runs parallel to $y = \frac{1}{2}x - 3$ and travels through the point $(6, 4)$ , apply the point-slope method. Step 1: Find the slope of the baseline equation. From $y = \frac{1}{2}x - 3$ , the slope is $m = \frac{1}{2}$ . Step 2: Determine the slope of the parallel line. Since parallel lines possess identical slopes, the parallel slope is $m_{\parallel} = \frac{1}{2}$ . Step 3: Note the required passing point, which is $(x_1, y_1) = (6, 4)$ . Step 4: Substitute the determined values into the point-slope form: $y - y_1 = m_{\parallel}(x - x_1)$ . This gives $y - 4 = \frac{1}{2}(x - 6)$ . Step 5: Write the result in standard slope-intercept form. Distribute the fraction $\frac{1}{2}$ into the parentheses to get $y - 4 = \frac{1}{2}x - 3$ . Add $4$ to both sides to cleanly detach $y$ , yielding the finalized equation: $y = \frac{1}{2}x + 1$ .

Updated 2026-05-03

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OpenStax Intermediate Algebra

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