Download Linear Test 2 Review

Linear Test 2 Review
Name: ______________________________________
Block: ____________ Date: ____________
It will cover:
*Parallel and Perpendicular lines
*Solving systems of equations (graphing)
*Function Questions (domain, range, x-int, y-int, zeros, inc/dec, end behavior, inverse)
*All linear forms (y = mx + b, Ax + By = C, and y –y1 = m(x – x1)
State whether each pair of lines is parallel, perpendicular, or neither.
1. y = ½ x – 5
2. 3x – 4y = 12
3. 10x – 5y = 20
y = -2x + 6
y = ¾ x + 10
-2x + y = -4
Perpendicular
Parallel
Parallel
4. Write an equation in slope-intercept form of a line that is a) parallel to and b) perpendicular to y = ¾ x – 3 and
goes through (2, -3).
a) Parallel equation: y =
3
x
4
-
9
2
b) Perpendicular equation: y =
−4
x
3
-
1
3
5. Write an equation in slope-intercept form of a line that is a) parallel to and b) perpendicular to 2x – 4y = 12 and
goes through (-4, - 6).
a) Parallel equation: y =
1
x
2
- 4
b) Perpendicular equation: y = -2x - 14
Fill in the table below answering each of the function questions.
6.
7.
6.
Is it a function? Why? Yes
Increasing/decreasing Inc(-00,00)
Domain
(-10,10)
Range
(-4.5,.5)
x-intercept
(8,0)
Zero
8
(0,-2)
y-intercept
As x →∞, y →
00
As x→-∞, y→
-00
Slope of the line
1/3
Equation in slopeY=1/3x -2
intercept form
7.
Yes
Constant
(-10,10)
(3)
None
None
(0,3)
3
3
0
Y=3
8.
8.
Yes
Dec(-00,00)
(-10,10)
(-10,6)
(-4,0)
-4
(0,-4)
-00
00
-1
Y=-1x - 4
Solve each system of equations. Some may be easier to use the substitution. Others may be easier to solve using the
graphing calculator. (Remember, for the graphing calculator, you have to rewrite into slope intercept form.)
9. y = 2x -5
y = -3x – 1
(.8, -3.4)
10. y = 3x + 1
-18x + 3y = 21
(-2,-5)
11. x = 2y + 4
2x – 6y = 18
(-6,-5)
Write an equation for each situation below. Don’t forget to label your axes!
12. Amanda is working out in the gym and wants to burn 500 calories. If she burns 50 calories an hour on the bike and
100 calories an hour on the treadmill, let y = the number of hours she rides the bike and x = the number of hours on the
treadmill. Write and graph an equation to represent this situation.
Equation: _____500=50y + 100x_______________________
13. A manager of a restaurant is placing an order for food. If donuts cost $10 per dozen and soup costs $12 per gallon,
let y = the number of dozens of donuts and x = the number of gallons of soup. Write and graph an equation for the
amount of food the manager can order if he wants to spend $180.
Equation: _____10y + 12x = 180________________________
Rewrite each equation into the form stated.
14. Rewrite into slope intercept and name the slope and y-intercept:
a. 5x – 8y = 20
b. 3x + 9y = 15
Y = 5/8x – 5/2
Slope = 5/8
y-int: -5/2
y = -1/3x + 15/9
slope= -1/3
y-int: 15/9
15. Rewrite into standard and name the x and y intercepts:
a. Y = 2/3 x – 9
b. y = -0.2x + 5
2x – 3y = 27
x-int: 27/2
y-int: -9
16. Rewrite into slope intercept:
a. Y – 9 = -2/3 (x – 5)
Y = -2/3x + 37/3
x + 5y = 25
x-int:25
y-int: 5
b. y + 5 = 5/2 (x – 3)
y = 5/2x – 25/2
What happens to the graph?
17. If we change the 5 to a 2 in the equation y = 5x – 6? The slope would be less steep
18. If we change the 1/6 to a 5/6 in the equation y = 1/6 x + 3? The slope would be more steep
19. If we change the 4 to a 9 in the equation y = -6x + 4? The line would shift up 5
On graph paper, graph the following equations:
20. A. 3x + 2y = 15
B. 4x – y = 7
21. A. y = -2/3 x + 1
B. y = 5/2 x – 3
22. A. y – 2 = ½ (x + 3)
B. y + 1 = -2(x – 4)
See end of page for answers.
Write an equation in slope intercept form that:
23. A. has a slope of ¾ and a y-intercept of 7
Y = 3/4x + 7
B. has a y-intercept of -2 and a slope of 4
y = 4x - 2
24. A. passes through the points (5, -2) and (1, -3)
Y = 1/4x – 13/4
B. passes through the points (0, 5) and (4, 8)
y = 3/4x + 5
25. Matches the tables given:
26. A.
y = 8x + 17
X
0
1
5
9
B. y = 6x – 4
Y
17
25
57
89
X
0
1
4
10
27. Complete the table
Equation
Y=6
Y=2
Y
-4
2
20
56
X = -2
X=4
Graph
Type of line
Slope
Horizontal
Horizontal through
(5,2)
Vertical
vertical
0
0
Undefined
undefined
28. Solve the following equations:
a. 8 = -3(x + 7)
b. 15 + 5x = 3 – 2x
X=-29/3
x=12/-7
c. 3(4m + 7) = 4(15 + 2m)
m=39/4
20 A.
B.
21 A.
B.
22A.
B.