chapter 4 – graphing linear equations 4.4 – the slope of a line
TRANSCRIPT
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
4.4 – The Slope of a Line
• 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
4.4 – The Slope of a Line
• 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.”
4.4 – The Slope of a Line
• When finding slope, the order of subtraction IS important.
• You must use the same order for subtracting in the numerator and the denominator.
4.4 – The Slope of a Line
• Example 1– Find the slope of the line passing
through (-3, 0) and (-1, 6).
4.4 – The Slope of a Line
• Example 2– Find the slope of the line passing
through (-1, -3) and (5, -3).
4.4 – The Slope of a Line
• Example 3– Find the slope of the line passing
through (-2, 1) and (1, -3).
4.4 – The Slope of a Line
• Example 4– Find the slope of the line passing
through (0, -1) and (0, 4).
4.4 – The Slope of a Line
• CLASSIFICATION OF LINES BY SLOPE– A line with positive slope rises from left to
right
4.4 – The Slope of a Line
• CLASSIFICATION OF LINES BY SLOPE– A line with negative slope falls from left to
right
4.4 – The Slope of a Line
• CLASSIFICATION OF LINES BY SLOPE– A line with undefined slope is vertical
4.4 – The Slope of a Line
• RATE OF CHANGE – compares two different quantities that are changing.
– Same as slope, but compares real-life quantities.
4.4 – The Slope of a Line
• 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.