Name________________________________
Date________________ Period_____
REVIEW Unit 4
I. Vocabulary
Go back and review your notes and class work along with the review to prepare
for your math test.
Direct variation
Rate of change
Constant of Variation
Slope
y-intercept
Perpendicular
Formulas:
What does m stand for?
y=mx + b
y − y1 = m( x − x1 )
Parallel
What does y stand for?
y = mx + b
m=
slope intercept
y2 − y1
x2 − x1 slope
y - y1 = m(x – x1) point-slope
Are the following direct variation? If yes, what is the constant of variation
(slope)?
1. y = 3x + 5
2. y = 2x
3
4
3. y = - x
4. Circle the graphs that are direct variation.
5. Direct variation equations all pass through the __________.
Find the rate of change AND explain what it means.
6. A school has 818 students attending in 1998 and 846 students attending in
2000. What is the rate of change?
7.
8.
Determine the slope between the given points.
* Use formula or calculator*
9. (-5, 7), (-1, 5)
m=
y2 − y1
x2 − x1
10. (0,4), (12, -3)
11. Undefined slope is a ______________ line.
12. zero (0) slope is a _____________ line.
Find the slope of each graph.
13.
Slope = ______
14.
Slope = ________
15.
Slope = _______
Through the given point, graph a line with the given slope.
Hint: Use formula
or plot point and then walk slope.
16. (3, -2); slope = -6
17. (-4, 7); slope =
5
2
Determine the equation of the line given the slope and y-intercept.
−4
; y-intercept is 1
5
18. Slope = 6; y-intercept is 7
19. Slope =
Equation: ________________
Equation: __________________
20. Slope =
5
; y-intercept is -2
3
Equation: _______________
21. Slope = -8; y-intercept is -10
Equation: __________________
Write an equation of a line with the given slope and y-intercept and graph each line.
22. m = 6, b = -4
2
23. m = - , b = 2
4
Equation: _______________
Equation: ________________
24-29. Graph each equation.
24. y =
1
x–4
3
27. 2x + 5y = -20
Get y by itself
25. y =
−7
x+3
2
28. y – x = 2
26. y = 2
29. 4x = 2y – 8
Get y by itself
Get y by itself
Write the equation of each graph below.
30.
31.
Equation: ________________
Equation: __________________
Determine the equation of the line given a point and slope. Put your answer
in slope-intercept form. Use point-slope formula.
32. (0, -12); m = -2
33. (5, -3); m = 2
Equation: ______________
Equation: __________________
Find the equation of a line that is parallel to the following equations and passes
through the point.
5
−5
34. (2, 7); y= x + 2
35. (-9, 8); y= x - 6
2
3
Equation: _______________
Equation: __________________
Find the equation of a line that is perpendicular to the following equations and
passes through the point.
36. ( 3, 1) y = 2x + 1
Equation: _______________
37.
(5, 1) y =
−5
x+8
3
Equation: __________________
Determine the equation of the line given two points.
1. Find slope
2. Plug 1 point and slope into formula y − y1 = m( x − x1 )
3. You may also use the STAT key on your calculator.
38. (4, 8), (2, 12)
39. (8, -2), (14, 1)
Equation: _______________
Equation: __________________
40. (-5, 13), (-10, 9)
41. (11, 7), (9, 3)
Equation: _______________
Equation: __________________
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
No
yes, 2
yes, -3/4
1st, last
origin
increase at a rate of 14
students per year
increased at a rate of 10
meters every 3 seconds
increased at a rate of 20
cookies baked per hour
-1/2
-7/12
vertical
horizontal
4
-1/5
6/7
17.
18.
19.
20.
21.
22.
y = -8x – 10
y = 6x – 4
23.
y = -1/2x + 2
24.
25.
y = 6x + 7
y = -4/5x + 1
y = 5/3x – 2
26.
35. y =
36.
37.
38.
39.
40.
41.
27. y = -2/5x – 4
28. y = x + 2
29. y = 2x + 4
30.
31.
32.
33.
y
y
y
y
=
=
=
=
34. y =
-x + 2
3/7x – 3 3/7
-2x – 12
2x – 13
5
+2
2
−5
x–7
3
y= -1/2x + 2.5
y= 3/5x -2
y = -2x + 16
y = 1/2x – 6
y = 4/5x + 17
y = 2x – 15