Download Sample Test 2, Math 58, Fall 2014

Math 58 Test # 4 Fall 2015
Chapter 10
Instructor: Smith-Subbarao
______SOLUTIONS________________
Name
Score: _______________
Percent: ______________
Directions:
 Show all work and circle/box your answers.

Partial credit may be given, even if the answer is incorrect, if your work is clear – attach
additional scratch pages you wish to be considered.

If you do not show your work, you may not get credit.

Unless otherwise instructed, leave all answers as fraction; improper fractions are OK.

Each problem is worth 5 points unless otherwise indicated
NO: Telephones, Books, Notes; CALCULATORS ARE NOT ALLOWEED
Suggestions:
 Choose the problems you understand best to work first.
 If you get stuck, write down what you do understand for partial credit and move on
 Show your work clearly
 Check your solutions
 Evaluate your solutions for “reasonableness”
1. Determine if the ordered pairs below solve the linear equation 4x – 2y = 8
a. (1, -2)
b. (4, -2)
4(1) – 2(-2) = 4+4 =8
yes
4(4) – 2(-2) = 16+4 = 20 ≠8
no
2. Fill in the table below with x and y values for the following equation: x/2 –y/3 = 6
x
0
2
-4
12
10
y
-18
-15
-24
0
-3
3. Plot the coordinate pairs from problem 2 on the graph below
Note that the points make a line!
4. Do the coordinate pairs given below satisfy the following equation? 5y/2 – 4 = 3x/4
a. (-6, 2)
5(2)/2 – 4 =1
3(-6)/4 = -9/2
no
b. (-12, -2)
5(-2)/2 -4 = -5 -4 = -9
3(-12)/4 = -39/4 = -9
yes
5. Give the quadrant of the following ordered pairs:
a. (-3/4, 8) Q2
b. (π, 9) Q1
c. (-4.28, -2.95) Q3
d. (95/2, 201/4) Q1
6. Find the x and y intercepts of the following equation: 2x – 3y = 12
x intercept: __(6,0)___________
y intercept:__(0, -4)________________
7. Find the x and y intercepts of the following equation: y = 3x + 12
x intercept: __(-4, 0)___________ y intercept:__( 0,12)________________
8. Using the points you found in problem 6, graph 2x – 3y = 12
You must use the intercepts from problem 6!
9. Indicate which the following points are on the line you graphed in problem 8:
a. (2, -8/3)
c. (5, 2/3)
2(2) +3(8)/3 = 12
2(5) – 3(2/3) = 10 – 2= 8
yes
no
10. (9, 2)
2(9) – 3(2) = 18-6 = 12
yes
d. (-3/2, -5)
2(-3/2) – 3(-5) = -3 + 15 = 12
yes
10. Using the points you found in problem 7, graph y = 3x + 12
Must use intercepts from problem 7
11. Write the equation of the line that has slope 3 and passes through the point (3,1)
y = mx + b = 3x + b
1 = (3)(3) + b = 9 + b
b = -8
y = 3x - 8
12. Give the x and y intercepts of the line in problem 11. Give your answer in the form of a
coordinate pair.
x intercept: _(8/3, 0)_________
y intercept: _(0, -8)_________
13. Find the slope of the line that passes through the following points:
a. (3, 2) and (5, 2)
m = (2-2)/(3-5) = 0
b. (-3, 0) and (-4, 8)
m = (0 – 8) / (-3 – (-4) = -8/1 = -8
14. Find the slope of the line that passes through the following points:
a. (5, -2) and (5, 3)
(-2 – 3) / (5 – 5) = -5/0, undefined – a vertical line
b. (-2, -5) and (-5, -2)
(-5 – (-2))/(-2 – (-5)) = -3 / 3 = -1
15. Write the equation for the lines in problem 13:
a. y = 2
b. y = -8x + b
0 = -8(-3) + b, b = 24
y = -8x + 24
16. Write the equation for the lines in problem 14:
a. x = 5
b. y = -x + b
-5 = -(-2) + b, b = -7
y = -x - 7
17. Are the following lines parallel, perpendicular, or neither:
a. y = 5x – 3 and 4y = 20x – 8
m = 5, m = 20/4 = 5, parallel
b. 3y = 2x and 2y = 3x
m = 2/3, m = 3/2, neither
c. 2y = -x + 2 and 2y = 4x + 9
m = -1/2, m = 2, perpendicular
d. 3y = 5x + 1 and 10y = 6x – 3
m = 5/3, m = 6/10 = 3/5, neither
18. Give the equation of the line in the following graph. HINT: Choose points that are
clearly at graph cross points so you don’t have to estimate values.
6
4
2
0
-6
-4
-2
-2
0
2
4
6
-4
-6
Clear points are (0,2) and (-2, -4), m = 3, and since we have (0, 2), b = 2; y = 3x + 2
19. Graph the following line: 2y = x - 4
20. Graph the line that has slope equal to 4 and passes through the point (-1, 4)