Chapter 7 Review

Multiple Choice
Identify the choice that best completes the statement or answers the question.

____	1.	Which letter represents the slope in the equation of a line, y = mx + b?
a.	b	c.	x	
b.	m	d.	y	

____	2.	Identify the equation of the line with a slope of –3 and a y-intercept of 4.
a.	y = 3x + 4	c.	y = –3x + 4	
b.	y = 3x – 4	d.	y = –3x – 4	

____	3.	Rewrite the equation y = –2x + 5 in general form.
a.	–2x + y – 5 = 0	c.	2x – y + 5 = 0	
b.	–2x – y + 5 = 0	d.	2x + y – 5 = 0	

____	4.	What is the equation y = 0.25x – 0.75 in general form?
a.	–x + 4y – 3 = 0	c.	x – 4y – 3 = 0	
b.	–x + 4y + 3 = 0	d.	x – 4y + 3 = 0	

____	5.	Which equation represents the line containing points M and N?

a.	y = –4x – 3	c.	y = x – 3	
b.	y = x – 3	d.	y = 4x – 3	

____	6.	Marie invested $800 in an account that pays 10% simple interest per year. The equation representing Marie’s investment is A = P + Prt, where A is the value of the investment, in dollars, P is the starting principle amount, in dollars, r is the interest rate written as a decimal, and t is the number of years the money is invested. How many years will pass before the investment is worth $1200?
a.	5	c.	25	
b.	10	d.	40	

____	7.	When a linear equation is written in the form Ax + By + C = 0, A and B cannot both be
a.	fractions	c.	one	
b.	integers	d.	zero	

____	8.	Rewrite the equation 4x + y + 2 = 0 in slope-intercept form.
a.	y = 4x + 2 	c.	y = –4x + 2	
b.	y = 4x – 2	d.	y = –4x – 2	

____	9.	Identify the slope and y-intercept of the relation represented by the equation 2x – 2y + 3 = 0.
a.	slope: 1, y-intercept: 	c.	slope: –1, y-intercept: 	
b.	slope: 1, y-intercept: 	d.	slope: –1, y-intercept: 	

____	10.	Points M(2, 9) and N(–1, 3) are on a line with y-intercept –4. What is the equation of the line?
a.	y = –4x – 2	c.	y = 2x – 4	
b.	y = –2x + 4	d.	y = 4x + 2	

____	11.	Identify the slope of the line through points (3, 4) and (–4, –5).
a.		c.	0	
b.	–1	d.		

____	12.	What value of q makes the line passing through  and  have a slope of 4?
a.		c.		
b.		d.		

____	13.	Using the table of values, determine the equation of the line.

a.	y = –3x – 9	c.	y = 3x – 9	
b.	y = –3x + 3	d.	y = 3x + 3 	

____	14.	The table of values represents a line. What is the equation of the line?

a.	y = 3x + 5	c.	y = –3x + 5	
b.	y = 3x – 5	d.	y = –3x – 5	

____	15.	The slope of the line that is perpendicular to the line y = x – 3 is
a.		c.		
b.		d.		

____	16.	In the graph, the equation of the line containing LM is y = 0.5x + 4. The two lines are parallel. What is the equation of the line containing NP?

a.	y = 0.5x – 2	c.	y = 2x – 2	
b.	y = 0.5x + 2	d.	y = 2x + 2	

____	17.	The equation of line T is y = 5x + 10, while the equation of line U is y = 4x + 10. Which statement is true?
a.	Line T is parallel to line U.	c.	Line T is steeper than line U.	
b.	Line U is perpendicular to line T.	d.	Line U is steeper than line T.	
Matching

Match each statement to the corresponding term. Each term may be used more than once or not at all.

a.	general form	g.	slope	
b.	negative reciprocals	h.	slope-intercept form	
c.	parallel lines	i.	slope-point form	
d.	perpendicular lines	j.	x-intercept	
e.	point of intersection	k.	y-intercept	
f.	reciprocals	

____	1.	For a horizontal line, this is zero.

____	2.	These lines have the same slope.

____	3.	For a vertical line, the value of x is constant and equal to this.

____	4.	This is where two lines meet.

____	5.	For the line y = 3x + 6, this is 6.

____	6.	The numbers 3 and  are examples.

____	7.	These lines meet at 90°.

____	8.	This is the name for an equation of a line in the form Ax + By + C = 0.

____	9.	This is the form usually used to show the equation of a line if you know the coordinates of the y-intercept and the slope.

____	10.	The numbers  and  are examples.

Short Answer

	1.	Determine the x-intercept and y-intercept of the line y = 1 – x. Then, graph the line.

	2.	a) What is the equation of the vertical line that passes through the point (3, 4)?
b) What is the equation of the horizontal line that passes through the point (3, 4)?

	3.	Write each equation in the form y = mx + b.
a) 3x + 2y – 4 = 0
b) x – 4y – 8 = 0

	4.	Determine the slope and draw the graph of a line with x-intercept 5 and y-intercept –3.

	5.	The slopes of each pair of lines are provided. Decide whether the lines in each pair are parallel, perpendicular, or neither. Justify your answers.
a) m =  and m = 
b) m = 100 and m = 0.01

c) m = 10 and m = –0.1

	6.	Jamie’s grandmother gave her $40 when she started high school. Jamie decided to add $5 a week toward the cost of a digital music player. Write an equation in the form Ax + By + C = 0 to represent Jamie’s savings.

	7.	Graph the equations y = x – 2 and x + y = 6. Then identify the point of intersection.

Problem

	1.	The distance-time graph illustrates Christine’s walk in front of a motion sensor. Her distance from the sensor, in metres, is represented by the variable d, and time, in seconds, is represented by t.

a) Identify the slope and d-intercept. Explain what they mean.
b) Write an equation in the form d = mt + b that describes Christine’s walk.
c) When was Christine 6 m from the sensor?

	2.	Danny works at a parking lot, where he can park his own car at a discounted rate. Whether he is working or not, he pays a flat fee of $2.00 plus $0.25 per hour that his car is parked. 
a) Write an equation to represent Danny’s total parking cost, C, in dollars, for t hours.
b) How much will it cost Danny to park his car for a full 24 h? 
c) If Danny has $6.00, for how many hours can he park his car in the parking lot?
Chapter 7 Review: Answer Section
MULTIPLE CHOICE

	1.	ANS:	B	PTS:	1	DIF:	A	OBJ:	Section 7.1
NAT:	RF6	TOP:	Slope-Intercept Form		KEY:	slope | equation of a line

	2.	ANS:	C	PTS:	1	DIF:	A	OBJ:	Section 7.1
NAT:	RF7	TOP:	Slope-Intercept Form		
KEY:	equation of a line | slope | y-intercept		

	3.	ANS:	D	PTS:	1	DIF:	B	OBJ:	Section 7.2
NAT:	RF6	TOP:	General Form			KEY:	general form | equation of a line

	4.	ANS:	C	PTS:	1	DIF:	D	OBJ:	Section 7.2
NAT:	RF6	TOP:	General Form			KEY:	general form | equation of a line

	5.	ANS:	B	PTS:	1	DIF:	B	OBJ:	Section 7.1
NAT:	RF7	TOP:	Slope-Intercept Form		
KEY:	slope-intercept form | graph | equation of a line

	6.	ANS:	A
Substitute the known values into the equation A = P + Prt:

The investment will be worth $1200 in 5 years.

PTS:	1	DIF:	C	OBJ:	Section 7.1	NAT:	RF5
TOP:	Slope-Intercept Form		KEY:	slope-intercept form | interest | problem solving

	7.	ANS:	D	PTS:	1	DIF:	B	OBJ:	Section 7.2
NAT:	RF1	TOP:	General Form			KEY:	general form | constraints

	8.	ANS:	D	PTS:	1	DIF:	A	OBJ:	Section 7.2
NAT:	RF6	TOP:	General Form			
KEY:	slope-intercept form | equation of a line	

	9.	ANS:	A	PTS:	1	DIF:	C	OBJ:	Section 7.2
NAT:	RF6	TOP:	General Form			
KEY:	slope-intercept form | slope | y-intercept	

	10.	ANS:	C	PTS:	1	DIF:	B	OBJ:	Section 7.3
NAT:	RF7	TOP:	Slope-Point Form		
KEY:	equation of a line given the slope and a point | slope-point form	

	11.	ANS:	D	PTS:	1	DIF:	B	OBJ:	Section 7.1
NAT:	RF3	TOP:	Slope-Intercept Form		KEY:	slope | ordered pairs

	12.	ANS:	A

	13.	ANS:	C

	14.	ANS:	B

	15.	ANS:	D
The slopes must be negative reciprocals, and the fraction  is the negative reciprocal of .

	16.	ANS:	A
Because the lines are parallel, they have the same slope of 0.5. The y-intercept of the line containing NP is –2. Substitute m = 0.5 and b = –2 into y = mx + b:
y = mx + b
y  = 0.5x – 2
The equation of the line containing NP is y = 0.5x – 2.

	17.	ANS:	C

MATCHING

	1.	ANS:	G	PTS:	1	DIF:	A	OBJ:	Section 7.1
NAT:	RF5	TOP:	Slope-Intercept Form		KEY:	slope | horizontal line

	2.	ANS:	C	PTS:	1	DIF:	A	OBJ:	Section 7.4
NAT:	RF3	TOP:	Parallel and Perpendicular Lines	KEY:	parallel lines | slope

	3.	ANS:	J	PTS:	1	DIF:	B	OBJ:	Section 7.1
NAT:	RF5	TOP:	Slope-Intercept Form		KEY:	slope | x-intercept | vertical line

	4.	ANS:	E	PTS:	1	DIF:	A	OBJ:	Section 7.4
NAT:	RF6	TOP:	Parallel and Perpendicular Lines	KEY:	point of intersection

	5.	ANS:	K	PTS:	1	DIF:	A	OBJ:	Section 7.1
NAT:	RF6	TOP:	Slope-Intercept Form		
KEY:	slope-intercept form | y-intercept | equation of a line

	6.	ANS:	F	PTS:	1	DIF:	A	OBJ:	Section 7.4
NAT:	RF3	TOP:	Parallel and Perpendicular Lines	KEY:	reciprocal

	7.	ANS:	D	PTS:	1	DIF:	A	OBJ:	Section 7.4
NAT:	RF3	TOP:	Parallel and Perpendicular Lines	KEY:	perpendicular lines

	8.	ANS:	A	PTS:	1	DIF:	A	OBJ:	Section 7.2
NAT:	RF6	TOP:	General Form			KEY:	general form | equation of a line

	9.	ANS:	H	PTS:	1	DIF:	A	OBJ:	Section 7.1
NAT:	RF6	TOP:	Slope-Intercept Form		
KEY:	slope-intercept form | equation of a line	

	10.	ANS:	B	PTS:	1	DIF:	A	OBJ:	Section 7.4
NAT:	RF3	TOP:	Parallel and Perpendicular Lines	
KEY:	negative reciprocal | perpendicular lines	

SHORT ANSWER

1.	ANS:	
Substitute y = 0 to find the x-intercept:
y = 1 – x
0 = 1 – x
x = 1 – x + x
x = 1
Substitute x = 0 to find the y-intercept:
y = 1 – x
y = 1 – 0
y = 1
The x-intercept is 1 and the y-intercept is 1.
Graph the ordered pairs (1, 0) and (0, 1). Then, draw the line that passes through these points:

	2.	ANS:	
a) x = 3
b) y = 4

	

	3.	ANS:	
a) 

b) 

	4.	ANS:	
Substitute the coordinates of the intercepts, (5, 0) and (0, –3), into the slope formula:

The slope is .
Use the intercepts to draw the graph:

	5.	ANS:	
a) 
The lines are parallel because they have the same slope.

b) The lines are neither perpendicular nor parallel because their slopes are not equal and their product is not –1.
c) The lines are perpendicular because their slopes are negative reciprocals. The product of the slopes is 10(–0.1) = –1.

	6.	ANS:	
Let the equation y = mx + b represent Jamie’s savings, where x represents the number of weeks, and y represents the amount of money, in dollars, Jamie has saved.. When x = 0, y = 40. Her weekly savings rate is the slope, so m = 5.
                y = 5x + 40
          y – y = 5x + 40 – y 
                0 = 5x + 40 – y 
5x – y + 40 = 0

	7.	ANS:	
Identify the x-intercept and y-intercept to graph the equations:
Substitute y = 0 into y = x – 2:
0 = x – 2
2 = x – 2 + 2
2 = x
Substitute x = 0 into y = x – 2:
y = 0 – 2
y  = –2
For y = x – 2, the x-intercept is 2 and the y-intercept is –2.
Substitute y = 0 into x + y = 6:
x + y = 6
x + 0 = 6
      x = 6
Substitute x = 0 into x + y = 6:
x + y = 6
0 + y = 6
      y = 6
For x + y = 6, the x-intercept and the y-intercept are both 6.

From the graph, the point of intersection is (4, 2).

PROBLEM

	1.	ANS:	
a) The slope is  and represents the distance, in metres, Christine walks away from the motion sensor in 1 s. 
The d-intercept is 2 and represents the distance, in metres, Christine was from the motion sensor when she started walking.

b) 

c) Substitute d = 6 into the equation from part b):

Sarah was 6 m from the sensor after approximately 2.7 s.

	2.	ANS:	
a) C = 0.25t + 2 

b) Substitute t = 24 into the equation C = 0.25t + 2:
C = 0.25t + 2
C = 0.25(24) + 2
C = 6 + 2
C = 8 
It will cost Danny $8.00 to park his car for 24 h. 

c) Substitute C = 6 into the equation C = 0.25t + 2:

Danny can park his car for 16 h if he has $6.00.