Quick answer

Plot y = mx + r, use slope a = -1/m through (x0, y0), mark where lines cross.

Formula

  • Rise/run for each slope
  • Intersection from algebra

Introduction

Graph after you solve so the picture matches the algebra. The calculator on the home page gives exact intersection coordinates to plot.

If you need reference values before you draw, scan the perpendicular line examples page for completed numeric cases.

Equal scales on both axes matter. A stretched axis can make a true right angle look wrong even when the slopes are correct.

For proof-style questions that connect graphs to distance or shapes, read perpendicular lines in coordinate geometry after you can plot both lines confidently.

Graphing workflow

Unequal axis scales can make a true 90-degree angle look wrong. Use consistent spacing when possible.

Plot the intersection first when you already solved for it; draw both lines through that anchor.

Color coding helps: one color for the base line, another for the perpendicular.

Rise-over-run triangles on each line reinforce the negative reciprocal relationship visually.

Formula and relationships

  • Rise/run for each slope
  • Intersection from algebra

Plot the intersection point first if you already solved it; draw both lines through that anchor.

Software tools still require you to choose the correct slopes; the program will not fix a wrong sign.

Graph paper makes integer slopes easier, while decimals may need a careful scale choice.

Step-by-step guide

  1. Draw the base line. Use m and r from y = mx + r.
  2. Plot the given point. Mark (x0, y0) clearly.
  3. Draw the perpendicular. Use slope a = -1/m from the point.
  4. Mark intersection. Label the coordinates on the grid.
  5. Check the corner. Compare to a right-angle template or square corner of paper.

Worked examples

y = x and y = -x + 2 cross at (1, 1) with perpendicular slopes 1 and -1.

A horizontal base y = 4 and perpendicular x = 2 through (2, 7) meet at (2, 4), forming a clear vertical crossing.

When algebra gives intersection (11/12, 13/12), plot the fraction carefully or use decimal approximations on software.