5. Determine whether the algebraic equation is linear.[latex]\,2x+3y=7[/latex]

6. Determine whether the algebraic equation is linear.[latex]\,6{x}^{2}-y=5[/latex]

7. Determine whether the function is increasing or decreasing.

<p style=”text-align: center”>[latex]f\left(x\right)=7x-2[/latex]

8. Determine whether the function is increasing or decreasing.

<p style=”text-align: center”>[latex]g\left(x\right)=-x+2[/latex]

9. Given each set of information, find a linear equation that satisfies the given conditions, if possible.

<p style=”text-align: center”>Passes through[latex]\,\left(\text{7},\text{5}\right)\,[/latex]and[latex]\,\left(\text{3},\text{17}\right)[/latex]

10. Given each set of information, find a linear equation that satisfies the given conditions, if possible.

<p style=”text-align: center”>x-intercept at[latex]\,\left(\text{6},0\right)\,[/latex]and y-intercept at[latex]\,\left(0,\text{1}0\right)[/latex]

11. Find the slope of the line shown in the graph.

12. Find the slope of the line graphed.

13. Write an equation in slope-intercept form for the line shown.

14. Does the following table represent a linear function? If so, find the linear equation that models the data.

15. Does the following table represent a linear function? If so, find the linear equation that models the data.

16. On June 1^st, a company has $4,000,000 profit. If the company then loses 150,000 dollars per day thereafter in the month of June, what is the company’s profit n^thday after June 1^st?

17. [latex]\begin{array}{c}2x-6y=12\\ -x+3y=1\end{array}[/latex]

18. [latex]\begin{array}{c}y=\frac{1}{3}x-2\\ 3x+y=-9\end{array}[/latex]

19. [latex]7x+9y=-63[/latex]

20. [latex]f\left(x\right)=2x-1[/latex]

21. Line 1: Passes through[latex]\,\left(5,11\right)\,[/latex]and[latex]\,\left(10,1\right)[/latex]

Line 2: Passes through[latex]\,\left(-1,3\right)\,[/latex]and[latex]\,\left(-5,11\right)[/latex]

22. Line 1: Passes through[latex]\,\left(8,-10\right)\,[/latex]and[latex]\,\left(0,-26\right)[/latex]

Line 2: Passes through[latex]\,\left(2,5\right)\,[/latex]and[latex]\,\left(4,4\right)[/latex]

23. Write an equation for a line perpendicular to[latex]\,f\left(x\right)=5x-1\,[/latex]and passing through the point (5, 20).

24. Find the equation of a line with a y– intercept of[latex]\,\left(0,2\right)\,[/latex]and slope[latex]\,-\frac{1}{2}.[/latex]

25. Sketch a graph of the linear function[latex]\,f\left(t\right)=2t-5.[/latex]

26. Find the point of intersection for the 2 linear functions:[latex]\,\begin{array}{c}x=y+6\\ 2x-y=13\end{array}.[/latex]

27. A car rental company offers two plans for renting a car.

Plan A: 25 dollars per day and 10 cents per mile

Plan B: 50 dollars per day with free unlimited mileage

How many miles would you need to drive for plan B to save you money?

28. Find the area of a triangle bounded by the y axis, the line[latex]\,f\left(x\right)=10-2x,[/latex] and the line perpendicular to[latex]\,f\,[/latex]that passes through the origin.

29. A town’s population increases at a constant rate. In 2010 the population was 55,000. By 2012 the population had increased to 76,000. If this trend continues, predict the population in 2016.

30. The number of people afflicted with the common cold in the winter months dropped steadily by 50 each year since 2004 until 2010. In 2004, 875 people were afflicted. Find the linear function that models the number of people afflicted with the common cold C as a function of the year,[latex]\,t.\,[/latex]When will no one be afflicted?

31. Find the linear function y, where y depends on[latex]\,x,[/latex] the number of years since 1980.

32. Find and interpret the y-intercept.
33. For the following exercise, consider this scenario: In 2004, a school population was 1,700. By 2012 the population had grown to 2,500. Assume the population is changing linearly.

1. How much did the population grow between the year 2004 and 2012?
2. What is the average population growth per year?
3. Find an equation for the population, P, of the school t years after 2004.

34. Find a formula for the moose population,[latex]\,P.[/latex]

35. What does your model predict the moose population to be in 2020?

36. In which subdivision have home values increased at a higher rate?

37. If these trends were to continue, what would be the median home value in Pima Central in 2015?

38. [latex]\begin{array}{l}3x-y=4\\ x+4y=-3\,\end{array}[/latex]and[latex]\,\left(-1,1\right)[/latex]

39. [latex]\begin{array}{l}6x-2y=24\\ -3x+3y=18\,\end{array}[/latex]and[latex]\,\left(9,15\right)[/latex]

40. [latex]\begin{array}{l}10x+5y=-5\hfill \\ \,\,\,3x-2y=-12\hfill \end{array}[/latex]

41. [latex]\begin{array}{l}\frac{4}{7}x+\frac{1}{5}y=\frac{43}{70}\\ \frac{5}{6}x-\frac{1}{3}y=-\frac{2}{3}\end{array}[/latex]

42. [latex]\begin{array}{l}5x+6y=14\\ 4x+8y=8\end{array}[/latex]

43. [latex]\begin{array}{l}3x+2y=-7\\ 2x+4y=6\end{array}[/latex]

44. [latex]\begin{array}{r}3x+4y=2\\ 9x+12y=3\end{array}[/latex]

45. [latex]\begin{array}{l}8x+4y=2\\ 6x-5y=0.7\end{array}[/latex]

46. A factory has a cost of production[latex]\,C\left(x\right)=150x+15\text{,}000\,[/latex]and a revenue function[latex]\,R\left(x\right)=200x.\,[/latex]What is the break-even point?

47. A performer charges[latex]\,C\left(x\right)=50x+10\text{,}000,\,[/latex]where[latex]\,x\,[/latex]is the total number of attendees at a show. The venue charges $75 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?