Graphing Linear Equations

Graph lines using slope-intercept form

Graphing Linear Equations

Slope-Intercept Form

y=mx+by = mx + b

where:

  • mm = slope (rise over run)
  • bb = y-intercept (where line crosses y-axis)

Finding Slope

Between points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

Types of Slopes

  • Positive: Line goes up left to right
  • Negative: Line goes down left to right
  • Zero: Horizontal line
  • Undefined: Vertical line

Graphing Steps

  1. Plot the y-intercept
  2. Use slope to find another point
  3. Draw the line

📚 Practice Problems

1Problem 1easy

❓ Question:

Find the slope and y-intercept of the line y=−3x+5y = -3x + 5

💡 Show Solution

The equation is already in slope-intercept form y=mx+by = mx + b

Compare y=−3x+5y = -3x + 5 with y=mx+by = mx + b:

  • Slope: m=−3m = -3
  • Y-intercept: b=5b = 5

This means:

  • The line has a slope of −3-3 (goes down 3 units for every 1 unit to the right)
  • The line crosses the y-axis at the point (0,5)(0, 5)

Answer: Slope = −3-3, y-intercept = 55

2Problem 2medium

❓ Question:

Find the slope of the line passing through (2,5)(2, 5) and (6,13)(6, 13)

💡 Show Solution

Use the slope formula: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

Identify the points: (x1,y1)=(2,5)(x_1, y_1) = (2, 5) and (x2,y2)=(6,13)(x_2, y_2) = (6, 13)

Substitute: m=13−56−2=84=2m = \frac{13 - 5}{6 - 2} = \frac{8}{4} = 2

Answer: The slope is 22

3Problem 3medium

❓ Question:

Convert 4x−2y=84x - 2y = 8 to slope-intercept form

💡 Show Solution

We need to solve for yy to get the form y=mx+by = mx + b

Step 1: Subtract 4x4x from both sides −2y=−4x+8-2y = -4x + 8

Step 2: Divide everything by −2-2 y=−4x+8−2y = \frac{-4x + 8}{-2} y=2x−4y = 2x - 4

Answer: y=2x−4y = 2x - 4 (slope = 22, y-intercept = −4-4)

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