1Cademy - Finding the Equation of a Line Parallel to $$y = 3x + 1$$ Through $$(4, 2)$$

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Finding an Equation of a Line Parallel to a Given Line

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Finding the Equation of a Line Parallel to $y = 3x + 1$ Through $(4, 2)$

To determine the equation of a line that is parallel to the line $y = 3x + 1$ and passes precisely through the point $(4, 2)$ , follow the procedure to write it in slope-intercept form. Step 1: Identify the slope of the original line. From the equation $y = 3x + 1$ , the slope is $m = 3$ . Step 2: Establish the parallel slope. Because parallel lines share the same slope, the new line will also have a slope of $m_{\parallel} = 3$ . Step 3: Identify the given coordinate. The specific point is $(x_1, y_1) = (4, 2)$ . Step 4: Substitute into the point-slope formula, $y - y_1 = m_{\parallel}(x - x_1)$ . Plugging in the values gives $y - 2 = 3(x - 4)$ . Step 5: Convert to slope-intercept form. Distribute the $3$ on the right side to get $y - 2 = 3x - 12$ . Then, isolate $y$ by adding $2$ to both sides, producing the final equation: $y = 3x - 10$ .

Updated 2026-05-03

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OpenStax Intermediate Algebra

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