Chapter 4 – Graphing Linear Equations 4.4 – The Slope of a Line

Chapter 4 – Graphing Linear Equations

4.4 – The Slope of a Line


• Today we will be:– Finding the slope of a line using two

of its points

– Interpret slope as a rate of change in real-life situations


• Slope – (m) – The number of units a nonvertical line rises or falls over the number of units the line changes from left to right.

• Two points on the line is all that is needed to find slope.

• SLOPE = rise run



• FINDING THE SLOPE OF A LINE– The slope m of a nonvertical line passing

through the points (x1, y1) and (x2, y2) is:•m = rise = change in y = y2 – y1

run change in x x2 – x1

• Read x1 as “x sub 1.” Think “x – coordinate of the first point.”

• Read y2 as “y sub 2.” Think “y – coordinate of the second point.”


• When finding slope, the order of subtraction IS important.

• You must use the same order for subtracting in the numerator and the denominator.


• Example 1– Find the slope of the line passing

through (-3, 0) and (-1, 6).



through (-1, -3) and (5, -3).



through (-2, 1) and (1, -3).



through (0, -1) and (0, 4).


• CLASSIFICATION OF LINES BY SLOPE– A line with positive slope rises from left to

right


• CLASSIFICATION OF LINES BY SLOPE– A line with negative slope falls from left to

right


• CLASSIFICATION OF LINES BY SLOPE– A line with zero slope is horizontal


• CLASSIFICATION OF LINES BY SLOPE– A line with undefined slope is vertical


• RATE OF CHANGE – compares two different quantities that are changing.

– Same as slope, but compares real-life quantities.


• Example 5– You are traveling by car and leave

your home at 8:00 a.m. By 8:45 a.m., you are 36 miles from home. Find the average speed in miles per hour.


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Chapter 4 – Graphing Linear Equations 4.4 – The Slope of a Line