Math 151 Review for Exam 1
Sketch the graph:
1. y  3x  5
5. y 
1
x 1
2
2. y 
1
x2
6. 4 x  3 y  6
3. y  x 3  3
4. y  x 2  4
7. xy  12
8. x 2 y  y  1
9. Which of the above equations are linear equations/
10. Find the following forms of the equation of the line through the points  1,4 and 3,5 :
(a) point-slope form. (b) slope-intercept form.
(c) general form.
Find the equation of the line (slope-intercept form where feasible):
11.
12.
13.
14.
15.
16.
17.
through the points  1,3 and 2,5 ,
through the points  1,4 and 3,4 .
through the points  1,4 and  1,5 .
with x-intercept 4 and y-intercept - 3.
with slope - 1 through the point 7,3 .
with slope  4 3 and x-intercept - 5.
with slope 5 2 and y-intercept 2.
18. Use the fact that the freezing point of water is 32oF and 0oC and the boiling point of water is
212oF and 100oC under normal conditions to derive a formula for converting from:
(a) Fahrenheit to Celsius.
(b) Celsius to Fahrenheit.
Solve the following systems graphically:
 4 x  3 y  8
 4x  2 y  6
19. 
20. 
 5x  2 y  9
 6 x  3 y  7
 9 x  6 y  12
21. 
 6 x  4 y  8
22. Solve problem 19 algebraically.
23. Solve problem 20 algebraically.
24. Solve problem 21 algebraically.
25. Suppose you rent a news stand for $350 and that you sell newspapers for 50 cents each and
that you pay 35 cents for each newspaper sold.
(a) Write an equation for your income with 2 unknowns.
(b) Write an equation for your expenses with the same 2 unknowns.
(c) Find out how many newspapers you need to sell in order to at least break even by solving the
above system algebraically.
(d) Draw a graph showing income, expenses, profit, loss, and break-even point.
Answers to Math 151 Review for Exam 1
1.
2.
3.
5., 8.
6.
4.
7.
9. equations 1 and 6.
10.(a) y  4   9  x  1 or y  5   9  x  3 (b) y   9 x 
4
4
4
11. y   8 x  1
3
3
15. y   x  4
12.
y4
16. y   4 x  20
3
3
13. x  1
17. y  5 x  2
2
18.(a) Freezing point is (32, 0). Boiling point is ( 212, 100).
(b) Freezing point is (0, 32). Boiling point is (100, 212).
7
4
(c)
9x  4 y  7
14. y  3 x  3
4
C  95 F  32 .
F  95 C  32 .
Answers to Math 151 Review for Exam 1
19. x  1 1 , y   1
2
2
22.
25.
x  11
, y   74
7
page two
20. no solution.
21. many solutions.
23. 0 = 4 ??? no solution.
24. 0 = 0 !!! many solutions.
(a) y  0.50 x
(b) y  350  0.35 x
(c) In theory at least 2333 1 newspapers. In practice at least 2334 newspapers.
3
(d)