Mrs. Agriesti's Algebra I Notes

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4.5 Quick Graphs Using the Slope-Intercept Form

Objective:

To use the slope-intercept form to graph linear equations.

Vocabulary:

• Slope - The ratio, m, of the vertical change to the horizontal change of a line.
  • It describes the rate of change or slant of the line.
  • Think of it as "rise over run".
• y-intercept - The point, b, where the line crosses the y-axis.
• slope-intercept form - y = mx + b, where m is the slope and b is the y-intercept.

Notes:

Steps to sketch the line:

1. Solve the equation for y (get y by itself) (if needed).
2. Plot the y-intercept, b, on the y-axis
3. Use the slope to plot a few more points.
   • Remember:

Examples:

Sketch each line:

1. 8x − 4y = 12
   
   • 
   • Now that the equation is in slope-intercept form you know that the slope is 2 and the y-intercept is −3.
   • Plot the y-intercept on the y-axis.
   • Use the slope to plot a few more points.
     • The positive slope tells us that the line will go up.
   • 
   
   

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2. 3x + 4y − 12 = 0
   
   • 
   • Now that the equation is in slope-intercept form you know that the slope is −3/4 and the y-intercept is 3.
   • Plot the y-intercept on the y-axis.
   • Use the slope to plot a few more points.
     • The negative slope tells us that the line will go down.
   • 
   
   
   

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To contact me:
email: michelle@agriesti.net