We must determine the length of her hair after 10 days, 60 days, and 90 days. We can organize the information in a table of values, shown below. x y 10 60 90 i) x 10: y 0.30x 250 y 0.30(10) 250 Substitute 10 for x. y 3 250 253 After 10 days, her hair is 253 mm long. We can write this as the ordered pair (10, 253). ii) x 60: y 0.30x 250 y 0.30(60) 250 Substitute 60 for x. y 18 250 268 After 60 days, her hair is 268 mm long. (Or, after about 2 months, her hair is about 10.5 in. long. It has grown about half of an inch.) We can write this as the ordered pair (60, 268). iii) x 90: y 0.30x 250 y 0.30(90) 250 Substitute 90 for x. y 27 250 277 After 90 days, her hair is 277 mm long. Write this as the ordered pair (90, 277). We can complete the table of values: x y 10 253 60 268 90 277 The ordered pairs are (10, 253), (60, 268), and (90, 277). b) Graph the equation. The x-axis represents the number of days after the hair was measured. Since it does not make sense to talk about a negative number of days, we will not continue the x-axis in the negative direction. The y-axis represents the length of the female’s hair. Likewise, a negative number does not make sense in this situation, so we will not continue the y-axis in the negative direction. The scales on the x-axis and y-axis are different. This is because the size of the numbers they represent are quite different. Here are the ordered pairs we must graph: (10, 253), (60, 268), and (90, 277). The x-values are 10, 60, and 90, so we will let each mark in the x-direction represent 10 units. The y-values are 253, 268, and 277. While the numbers are rather large, they do not actually differ by much. We will begin labeling the y-axis at 250, but each mark in the y-direction will represent 3 units. Because there is a large jump in values from 0 to 250 on the y-axis, we indicate this with “ ” on the axis between the 0 and 250. Notice, also, that we have labeled both axes. The ordered pairs are plotted on the graph shown at the left, and the line is drawn through the points. Length of Hair (10, 253) 10 20 30 40 50 (90, 277) (60, 268) 60 70 80 90 100 Days 280 277 274 271 268 265 262 259 256 253 250 0 Length (in mm) 148 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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