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Chapter 8
Graphing Linear Equations
§8.1 – Linear Equations in 2 Variables
• What is an linear equation? What is a
solution?
3x = 9
• What is an linear equation in 2 variables?
What is a solution?
2x + y = 10
§8.1 – Linear Equations in 2
Variables
• Linear equations in 2 variables
– Ordered pairs
– Complete ordered pair given one of the values
• Rectangular coordinate system structure
– Axes and quadrants
– Plotting points
– Determining coordinates of plotted points
§8.2 – Graphing Linear Equations
• Algorithm on p. 285
1. Find 3 solutions
2. Plot corresponding points
3. Draw line thru points
• If not straight – find your error
• Ex: Graph 3x + 2y = 12
• x and y intercepts
§8.2 – Graphing Linear Equations
• Horizontal lines
y=a
• Vertical lines
x=b
• Problem #42 p. 290
– Why only positive values?
§8.3 – The Slope of a Line
• What is slope?
rise y2  y1

• Slope formula: slope  m 
run x2  x1
• General concepts
– Positive slope
– Negative slope
– 0 slope
– Undefined slope
§8.3 – The Slope of a Line
• Slope – intercept form: y  mx  b
• General concepts
– y isolated
– m is the slope
– b is the y–intercept
§8.3 – The Slope of a Line
• For each of the following lines, find the slope,
the y–intercept, and graph the line
y  23 x  4
3x  7 y  8
§8.3 – The Slope of a Line
• Parallel lines
– What are they?
– Same slope
– Problems 8.3 #31, 32 (p. 297) – just parallel
• Perpendicular lines
– What are they?
– Slopes are negative reciprocals of each other
– Problems 8.3 #31, 32 (p. 297) – just perpendicular
§8.4 – The Equation of a Line
• Slope – intercept form: y  mx  b
– Find equation given m and b
• Problem 8.4 #22 (p. 301)
• Point – Slope form: y  y1  m( x  x1 )
– Find equation given point and slope
• Problem 8.4 #32 (p. 301)
– Find equation given 2 points
• Problem 8.4 #52 (p. 301)