1Cademy - Finding the Equation of a Line Perpendicular to $$y = 2x

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Finding an Equation of a Line Perpendicular to a Given Line

Example

Finding the Equation of a Line Perpendicular to $y = 2x - 3$ Through $(-2, 1)$

To calculate the equation of a line perpendicular to $y = 2x - 3$ that intersects the coordinate plane at the point $(-2, 1)$ , follow the five-step procedure for perpendicular lines. Step 1 — Find the original slope. The given equation is $y = 2x - 3$ . Because it is provided in slope-intercept form, the slope is readily apparent: $m = 2$ . Step 2 — Determine the perpendicular slope. Perpendicular lines meet at right angles and therefore have negative reciprocal slopes. Taking the opposite reciprocal of $2$ dictates that the new slope is $m_{\perp} = -\frac{1}{2}$ . Step 3 — Identify the specific point. The perpendicular line is required to pass through $(x_1, y_1) = (-2, 1)$ . Step 4 — Substitute these values into the point-slope form. Use the equation template $y - y_1 = m(x - x_1)$ : $y - 1 = -\frac{1}{2}(x - (-2))$ Simplify the double negative inside the parentheses into addition: $y - 1 = -\frac{1}{2}(x + 2)$ Distribute the $-\frac{1}{2}$ systematically across the binomial elements: $y - 1 = -\frac{1}{2}x - 1$ Step 5 — Write in slope-intercept form. To strictly isolate $y$ , logically add $1$ to both sides of the equality: $y = -\frac{1}{2}x$ The final algebraic expression for the requested perpendicular line is $y = -\frac{1}{2}x$ .

Updated 2026-05-03

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