Graphing Equations in Point-Slope Form

Introduction

• Understanding how to graph a linear equation given in point-slope form.

Steps to Graph a Point-Slope Equation

Identify Key Elements

1. Identify the Slope (m):
   • The slope is the coefficient of x in the equation.
2. Identify the Point (x1, y1):
   • The point is represented by the ordered pair derived from the equation.
   • Change the signs of the constants in the equation to find x1 and y1.

Example 1

• Given Equation: y - 3 = 2(x - 1)
  • Slope (m): 2
  • Point (x1, y1): (1, 3)

Plotting the First Point

• Plot the point (1, 3) on the coordinate plane.

Using the Slope

• With a slope of 2, move:
  • 1 unit right (increase x by 1)
  • 2 units up (increase y by 2)
• Next Point: (2, 5)
• To find another point, move:
  • 1 unit left (decrease x by 1)
  • 2 units down (decrease y by 2)
• Connect the points with a straight line.

Example 2

• Given Equation: y + 3 = (3/2)(x + 4)
  • Slope (m): 3/2
  • Point (x1, y1): (-4, -3)

Plotting the First Point

• Plot the point (-4, -3) on the coordinate plane.

Using the Slope

• With a slope of 3/2, move:
  • 2 units right (increase x by 2)
  • 3 units up (increase y by 3)
• Next Point: (-2, 0)
• To find another point, move:
  • 2 units right (increase x by 2)
  • 3 units up (increase y by 3)
• Next Point: (0, 3)
• Connect the points with a straight line.

Summary

• To graph a linear equation in point-slope form:

  1. Find the point (x1, y1).
  2. Determine the slope (m).
  3. Use the slope to find at least one more point.
  4. Connect the points with a straight line.

• Minimum requirement: Two points are needed to draw a straight line.