Write The Equation Of A Line Parallel To The Given Line

Question

Write the equation of a line parallel to the given line and Write the equation of a line parallel to the given line and passing through the given point. Write the equation of a line perpendicular to the given line and passing through the given point. Given pairs: 1) y = 1/2 x + 3; (-2, 1) 2) y = -2x - 4; (1, 3) 3) y = 1/4 x - 2; (8, -1) 4) y = -x + 3; (-2, -2) 5) y = -1/3 x - 4; (-6, -3) 6) y = -1/2 x + 1; (4, 2) 7) y = 3/4 x - 1; (4, 0) 8) y = 3x + 3; (1, 1) 9) y = -4x - 5; (0, -1) 10) y = -2/5 x + 2; (9, -3) 11) y = 2x - 1; (2, -2) 12) y = -3x - 6; (-1, 5) 13) y = x + 4; (-7, 1) 14) y = 3/4 x - 1; (3, 1) 15) y = 3x + 3; (-1, -1) 16) y = -4x - 5; (-1, 0) 17) y = -2/5 x + 2; (6, 3) 18) y = 2x - 1; (-2, 2) 19) y = -3x - 6; (-3, 2) 20) y = x + 4; (1, -7) 21) y = 1/2 x + 3; (4, -1) 22) y = -2x - 4; (2, -3) 23) y = -1/4 x - 2; (-8, 1) 24) y = -x + 3; (2, 2) 25) y = -1/3 x - 4; (3, 1) 26) y = -1/2 x + 1; (-2, 3) 27) y = 1/4 x + 1; (-4, 3) 28) y = 5x - 1; (5, -8) 29) y = x + 7; (-7, 1) 30) y = 1/2 x + 3; (-6, -7) 31) y = -2x + 5; (3, 0) 32) y = -1/3 x + 3; (6, -4) 33) y = 1/3 x + 2; (6, -3) 34) y = 2x; (-3, -3) 35) y = 5; (4, 4) 36) y = -x + 7; (-7, -1) 37) y = -5x - 1; (5, 9) 38) y = -3/4 x - 1; (12, 5) 39) y = 1/3 x + 2; (-6, 3) 40) y = x; (0, 0)

Dr. Jack HW Helper · Accepted Answer

Overview This document explains the method for writing the equation of a line parallel to a given line and passing through a specified point, and the equation of the line perpendicular to the same given line and passing through the same point. The standard slope-intercept form y = m x + b is used to identify slope (m). Parallel lines share the same slope; perpendicular lines have slope equal to the negative reciprocal of the original slope (except in the vertical/horizontal special cases) (Khan Academy, 2020; Paul Dawkins, 2006). General method Given a line in slope-intercept form y = m x + b and a point (x1, y1): Parallel line: slope = m. Use point-slope form: y - y1 = m(x - x1). Solve for y to get y = m x + b_parallel (Paul Dawkins, 2006). Perpendicular line: slope = -1/m (for m ≠ 0). Use point-slope: y - y1 = (-1/m)(x - x1). Solve for y to get y = (-1/m) x + b_perp. If m = 0 (horizontal), the perpendicular is a vertical line x = x1; if the original line is vertical (x = c), the perpendicular is horizontal y = y1 (Stewart, 2015; Purplemath, 2018). This point-slope approach is a standard technique in analytic geometry and is widely documented (Abramson, 2016; Wolfram MathWorld, 2019). Worked example (step-by-step) Example 1 (pair 1): Given y = (1/2) x + 3 and point (-2, 1). The original slope m = 1/2. - Parallel: slope = 1/2. Point-slope: y - 1 = (1/2)(x + 2) ⇒ y = (1/2)x + 2. - Perpendicular: slope = -2 (negative reciprocal of 1/2). Point-slope: y - 1 = -2(x + 2) ⇒ y = -2x - 3. Example 2 (special case, pair 35): Given y = 5 (slope 0) and point (4, 4). - Parallel: slope 0, so the line passing through (4,4) is y = 4 (horizontal). - Perpendicular: vertical line through x = 4: x = 4 (vertical lines are expressed as x = constant) (Kendall et al., 2014). Complete solutions (parallel and perpendicular equations) The following concise list gives the parallel and perpendicular lines for each numbered pair. Each result is computed from point-slope form and simplified to slo

Write The Equation Of A Line Parallel To The Given Line ✓ Solved

Write the equation of a line parallel to the given line and

Paper For Above Instructions

Overview

General method

Worked example (step-by-step)

Complete solutions (parallel and perpendicular equations)

Conclusion

References