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Slopes of Lines in the Coordinate Plane For Exercises
Slope =
Find the point where the line through
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- The point-slope form of the equation of the line with slope 3 passing through the point 1, 2 is _.arrow_forwardWhen Date Are Unevenly speed. If data are evenly spaced, we need only calculate differences to see whether the data are linear. But if data not evenly spaced, then we must calculate the average rate of change over each interval to see whether the data are linear. If the average rate of changes is constant, it is the slope of the linear function. This fact is used in Exercises 23 and 24. In the following table, show that the average rate of change is the same over each interval. This shows the data are linear, even though the differences in y are not constant. Then find a linear model for the data. x 1 2 5 6 y 7 10 19 22arrow_forwardWhen Date Are Unevenly speed. If data are evenly spaced, we need only calculate differences to see whether the data are linear. But if data are not evenly spaced, then we must calculate the average rate of change over each interval to see whether the data are linear. If the average rate of change is constant, it is the slope of the linear function. This fact is used in Exercises 23 and 24. In the following table, show that the average rate of change from 2 to 5 is not the same as the average rate of change from 5 to 6. This shows that the data are not linear, even though the differences in y are constant. x 1 2 5 6 y 3 6 9 12arrow_forward
- Does the following table represent a linear function ? If so, find the linear equation that models the data.arrow_forwardEmployee Turnover The percentage of employees who cease their employment during a year is referred to as employee turnover, and it is a serious issue for businesses. The following table shows the cost, in millions of dollars, to Walmart for a given employee turnover percentage in a year.13 E = employee turnover 10 20 30 40 C = cost 250 400 550 700 a. Show that the data can be modeled by a linear function. b. Find the slope of the linear function. c. Find a linear model for the data. d. Use the result from part c to find the cost to Walmart if employee turnover is 33 in a year.arrow_forwardSlope If a building is 100 feet tall and is viewed from a spot on the ground 70 feet away from the base of the building, what is the slope of a line from the spot on the ground to the top of the building?arrow_forward
- Slopes of Lines in the Coordinate Plane For Exercises S-14 through S-25, use the fact that for points (a1,b1) and (a2,b2) in the coordinate plane, we can calculate the slope of the line through these points using Slope = yx=b2b1a2a1. Find the slope of the line through the points (3.6,2.5)and(2.4,1.6).arrow_forwardSuppose that average annual income (in dollars) forthe years 1990 through 1999 is given by the linearfunction: I(x)=1,054x+23,286 , where x is thenumber of years after 1990. Which of the followinginterprets the slope in the context of the problem? a. As of 1990, average annual income was $23,286. b. In the ten-year period from 1990-1999, averageannual income increased by a total of $1,054. c. Each year in the decade of the 1990s, averageannual income increased by $1,054. d. Average annual income rose to a level of $23,286 bythe end of 1999.arrow_forwardLife Expectancy Versus Health Care Spending One article shows a relationship between per capita health care spending h, in thousands of U.S. dollars per person per year, and life expectancy E, in years. The following formula is adapted from that article: E=72.23+3.85h0.37h2 We should point out that this article includes no justification for the type of model used. a.Plot the graph E versus h. Include spending levels from 1000 to 9000 per person per year so a horizontal span of 1 to 9. b. According to this model, what health care expenditure corresponds to maximum longevity? Round your answer in thousands of dollars per person per year to two decimal places. c.What optimum life expectancy is given by this model? For comparison, in 2011, in the United States, per capita health care spending was 8745 and life expectancy was 78.7 years.arrow_forward
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