Lesson 3-3: Graphing Linear Equations — MathPath

Method 1

Using Slope-Intercept Form

For $y = mx + b$ :

1. Plot the y-intercept (0, b) 2. From that point, apply slope: rise m, run 1 3. Plot that second point 4. Draw a straight line through both points

Example: Graph $y = 2x - 1$ . Start at (0, −1). Go up 2, right 1 → plot (1, 1). Draw the line.

Method 2

Using x- and y-Intercepts

Set x=0 to find the y-intercept. Set y=0 to find the x-intercept. Plot both and draw the line.

Example: Graph $2x + 3y = 12$ .

1. y-intercept: set x=0 \to 3y=12 \to y=4 \to point (0, 4) 2. x-intercept: set y=0 \to 2x=12 \to x=6 \to point (6, 0) 3. Plot (0,4) and (6,0), draw line through them

Special Lines

Parallel and Perpendicular Lines

Parallel lines have the same slope and different y-intercepts. They never intersect.
Perpendicular lines have slopes that are negative reciprocals: if one has slope m, the other has slope −1/m.

y = 3x + 1 and y = 3x - 4 \to parallel (both m = 3) y = 2x + 1 and y = -½x + 3 \to perpendicular (2 \times -½ = -1)

Your Turn

Try It Yourself

Q: Find the slope of a line perpendicular to $y = 4x - 3$ .

Show Answer

Original slope = 4. Perpendicular slope = −1/4.

Key Takeaways

1-Minute Summary

Slope-intercept: plot b, then use slope to get a second point
Intercept method: find (0, y) and (x, 0), then connect them
Parallel lines: same slope. Perpendicular lines: slopes are negative reciprocals.

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