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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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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- 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 point where the line through (1.1,3.6) with slope 2.3 crosses the vertical axis.arrow_forwardSlopes 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 (5,2) and (6,9).arrow_forwardSlopes 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 point where the line through (1,4) with slope 2 crosses the horizontal axis. Suggestion: The line must fall by 4 units to reach the horizontal axis.arrow_forward
- Maximum Sales Growth This is a continuation of Exercise 10. In this exercise, we determine how the sales level that gives the maximum growth rate is related to the limit on sales. Assume, as above, that the constant of proportionality is 0.3, but now suppose that sales grow to a level of 4 thousand dollars in the limit. a. Write an equation that shows the proportionality relation for G. b. On the basis of the equation from part a, make a graph of G as a function of s. c. At what sales level is the growth rate as large as possible? d. Replace the limit of 4 thousand dollars with another number, and find at what sales level the growth rate is as large as possible. What is the relationship between the limit and the sales level that gives the largest growth rate? Does this relationship change if the proportionality constant is changed? e. Use your answers in part d to explain how to determine the limit if we are given sales data showing the sales up to a point where the growth rate begins to decrease.arrow_forwardProperties of Linear Functions Exercises S-15 through S-27 explore elementary properties of linear functions. If x is increased by 7 units, y is increased by 9 units. If x is increased by an additional 7 units, y is increased by only 8 units. Is y a linear function of x?arrow_forwardSlope from Two Values Suppose that f is a linear function such that f(2)=7 and f(5)=19. What is the slope of f?arrow_forward
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