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messersmith_power_intermediate_algebra_1e_ch4_7_10

Use two clearly defined points on the line to find the slope. Note that the numerator of the slope ratio will always represent the vertical change, and the denominator will always represent the horizontal change! 1 Understand the Concept of Slope In Section 4.1, we learned to graph lines by plotting points. You may have noticed that some lines are steeper than others. Their “slants” are different too. t t t x y t x y t t t t x y t y t We can describe the steepness of a line with its slope. Property Slope of a Line The slope of a line measures its steepness. It is the ratio of the vertical change in y to the horizontal change in x. Slope is denoted by m. We can also think of slope as a rate of change. Slope is the rate of change between two points. More specifi cally, it describes the rate of change in y to the change in x. y 5 2 5 t t 5 5 2 1 x 5 1 t x y t 2 1 2 Slope 3 5 dd vertical change horizontal change Slope 4 or 4 1 dd vertical change horizontal change For example in the graph on the left, the line changes 3 units vertically for every 5 units it changes horizontally. Its slope is 3 5 . The line on the right changes 4 units vertically for every 1 unit of horizontal change. It has a slope of 4 1 or 4. Notice that the line with slope 4 is steeper than the line that has a slope of 3 5 . x Note As the magnitude of the slope gets larger the line gets steeper. Here is an application of slope. 156 CHAPTER 4 Linear Equations in Two Variables and Functions www.mhhe.com/messersmith


messersmith_power_intermediate_algebra_1e_ch4_7_10
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