1. Write the coordinates of point A.
A coordinate grid is shown with x- and y-axes between negative 6 to 6 with each interval mark representing one unit. Point A is labeled four interval marks to the left of the y-axis and one interval mark above the x-axis. (1 point)
(1, –4)
(–4, –1)
(4, 1)
(–4, 1)
2. Laura is designing a rectangular porch for her house. On her scale drawing, the vertices of the rectangle are (2, 7), (8, 7), and (2, 9). What are the coordinates of the fourth vertex? (1 point)
(8, 9)
(7, 9)
(7, 2)
(2, 8)
3. Determine which ordered pair is not a solution of y = –5x – 4. (1 point)
(10, –52)
(7, –39)
(–7, 31)
(8, –44)
4. Which is the graph of the linear equation y = –one-thirdx + 5? (1 point)
A line is graphed on a coordinate plane. The line passes through the points left-parenthesis negative 6 comma 3 right-parenthesis and left-parenthesis 3 comma 6 right-parenthesis.
A line is graphed on a coordinate plane. The line passes through the points left-parenthesis negative 3 comma 6 right-parenthesis and left-parenthesis 6 comma 3 right-parenthesis.
A line is graphed on a coordinate plane. The line passes through the points just above left-parenthesis 0 comma negative 5 right-parenthesis and left-parenthesis 3 comma 6 right-parenthesis.
A line is graphed on a coordinate plane. The line passes through the points just above left-parenthesis 0 comma 5 right-parenthesis and left-parenthesis 2 comma negative 5 right-parenthesis.
5. Find three solutions of the equation y = 7x – 5. (1 point)
(3, –26), (–1, –12), (3, 16)
(–3, –26), (–12, –1), (16, 3)
(–3, –26), (3, 16), (1, –12)
(–3, –26), (–1, –12), (3, 16)
6. Which pair of points has a positive slope? (1 point)
(–2, 9), (1, –9)
(–2, 5), (2, –11)
(–2, –15), (4, 21)
(–2, 13), (1, –11)
7. Use integer values of x from –3 to 3 to graph the equation.
y = –|x| (1 point)
graph A Its vertex is at left parenthesis 0 comma 0 right parenthesis. It passes through left parenthesis negative 5 comma 5 right parenthesis and through left parenthesis 5 comma 5 right parenthesis.
graph BIts vertex is at left parenthesis 0 comma 0 right parenthesis. It passes through left parenthesis negative 5 comma negative 5 right parenthesis and through left parenthesis 5 comma negative 5 right parenthesis.
graph CIts vertex is at left parenthesis 0 comma 0 right parenthesis. It passes through left parenthesis negative 2 comma negative 4 right parenthesis and through left parenthesis 2 comma negative 4 right parenthesis.
graph DIts vertex is at left parenthesis 0 comma 0 right parenthesis. It passes through left parenthesis negative 2 comma 4 right parenthesis and through left parenthesis 2 comma 4 right parenthesis.
8. The ordered pairs (2, –17) and (5, –35) are solutions to which of the following equations? (1 point)
y = –6x + 5
y = 6x – 5
y = 6x + 5
y = –6x – 5
9. Which is a rule that describes the translation of a point from (–5, 4) to (–1, 2)? (1 point)
(x, y) arrow(x – 4, y – 2)
(x, y) arrow(x + 4, y – 2)
(x, y) arrow(x + 4, y + 2)
(x, y) arrow(x – 4, y + 2)
10. Δ JKL has vertices J(10, 5), K(2, 8), and L(4, 9). It is translated right 5 units and up 4 units. What are the coordinates of J’, K’, and L’? (1 point)
J' (15, 9), K' (12, 7), L' (9, 13)
J' (15, 9), K' (7, 12), L' (9, 13)
J' (14, 10), K' (6, 13), L' (10, 12)
J' (15, 5), K' (7, 8), L' (9, 9)
11. The point Q left parenthesis 9 comma negative 1 right parenthesis is reflected across the y-axis. Use arrow notation to describe the original point and its reflection. (1 point)
Q left parenthesis 9 comma negative 1 right parenthesis right-arrow Q prime left parenthesis 9 comma 1 right parenthesis
Q left parenthesis 9 comma negative 1 right parenthesis right-arrow Q prime left parenthesis negative 9 comma 1 right parenthesis
Q left parenthesis 9 comma negative 1 right parenthesis right-arrow Q prime left parenthesis negative 9 comma negative 1 right parenthesis
Q left parenthesis 9 comma negative 1 right parenthesis right-arrow Q prime left parenthesis 9 comma negative 1 right parenthesis
12. The coordinates of three vertices of a rectangle are shown on the grid.
A coordinate graph with x and y axes labeled from negative 5 to 5 is shown with a black dots at the points negative 1 comma negative 2, negative 1 comma 4, and 3 comma 4.
Which could be the coordinates of the fourth vertex?
(1 point)
(3, –2)
(3, –1)
(–2, 3)
(4, –2)
13. Draw the image of the figure after a rotation of 180º around O.
An isosceles trapezoid LMNO is shown with segment LM as the shorter base and ON and the longer base. (1 point)
Two trapezoids are graphed on a coordinate grid.Trapezoid LMNO is graphed on a coordinate grid. Trapezoid L prime M prime N prime O prime shares a single point, O, with LMNO and appears to have exactly the same shape and proportions. However, L prime M prime N prime O prime shares point O/O prime with LMNO and is upside down.
Two trapezoids are graphed on a coordinate grid.Trapezoid LMNO is graphed on a coordinate grid. Trapezoid L prime M prime N prime O prime shares a single point, O, with LMNO and appears to have exactly the same shape and proportions. However, L prime M prime N prime O prime is on its side, with the shorter parallel side of the trapezoid pointing right.
Two trapezoids are graphed on a coordinate grid.Trapezoid LMNO is graphed on a coordinate grid. Trapezoid L prime M prime N prime O prime shares a single point, O, with LMNO and appears to have exactly the same shape and proportions. L prime M prime N prime O prime is immediately to the right of LMNO.
Two trapezoids are graphed on a coordinate grid.Trapezoid LMNO is graphed on a coordinate grid. Trapezoid L prime M prime N prime O prime shares a single point, O, with LMNO and appears to have exactly the same shape and proportions. L prime M prime N prime O prime is immediately to the right of LMNO and on its side, with the shorter parallel side on the left.
14. Which table shows a proportional relationship? (1 point)
X 1 3 4 6
Y –11 –23 –29 –41
X 1 3 4 6
Y 2 –10 –16 –28
X 1 3 4 6
Y –6 –22 –30 –46
X 1 3 4 6
Y –8 –24 –32 –48
15. Identify the unit rate shown in the graph.
A graph is shown with the x axis labeled number of miles and the y axis labeled gallons of gas. The x-axis goes from 0 to 100 and the y-axis goes from 0 to 6. The graph is a straight line that goes through the points left-parenthesis 30 comma 2 right-parenthesis and left-parenthesis 60 comma 4 right-parenthesis. (1 point)
15 gallons per mile
8 miles per gallon
15 miles per gallon
8 gallons per mile
16. The graph below shows Cara's earnings according to the number of hours she works.
A coordinate graph is shown.
What does the slope of the line represent?
(1 point)
For every $50 Cara earns, she works 10 hours.
For every $50 Cara earns, she works 3 hours.
For each hour Cara works, she earns $10.
For each hour Cara works, she earns $15.
17. Which of the following is a graph of y = x2? (1 point)
This is a graph of a parabola that passes through the points left parenthesis negative 2 comma 2 right parenthesis, left parenthesis 0 comma 0 right parenthesis, and left parenthesis 2 comma 2 right parenthesis.
This is a graph of a parabola that passes through the points left parenthesis negative 2 comma 4 right parenthesis, left parenthesis 0 comma 0 right parenthesis, and left parenthesis 2 comma 4 right parenthesis.
This is a graph of a parabola that passes through the points left parenthesis negative 2 comma 8 right parenthesis, left parenthesis 0 comma 0 right parenthesis, and left parenthesis 2 comma 8 right parenthesis.
This is a graph of a parabola that passes through the points left parenthesis negative 2 comma 6 right parenthesis, left parenthesis 0 comma 0 right parenthesis, and left parenthesis 2 comma 6 right parenthesis.
18. The table shows the amount of money Angelica earned based on the number of hours she worked.
Angelica's Pay
Hours Worked (h) Amount Earned (A)
3 $22.50
8 $60.00
15 $112.50
Which equation best represents Angelica's pay?
(1 point)
A = 7.50h
A = 22.50h
A = h + 7.50
A = h + 22.50
Short Answer
1. Write the slope-intercept form of the equation of a line that passes through the point (4, 6) and has a slope of -2. (2 points)
y = -2x + 14
2. Find the midpoint between the points (-3, 2) and (7, -6). (2 points)
(2, -2)
3. Given the equation y = 2x - 5, find the y-coordinate when x = 3. (2 points)
y = 1
4. Determine the equation of the line that is perpendicular to y = 2x + 4 and passes through the point (1, 3). (3 points)
The slope of the original line is 2, so the slope of the perpendicular line is -1/2. Using the point-slope form of the equation for a line:
y - 3 = (-1/2)(x - 1)
y = (-1/2)x + 4.5
5. A rectangle has vertices at (1, 2), (1, 6), (5, 6), and (5, 2). Determine the length of its longer diagonal. (3 points)
Using the distance formula:
d = sqrt((5-1)^2 + (6-2)^2) = 2sqrt(10)
6. A car rental company charges a base rate of $20 per day plus $0.15 per mile driven. Write an equation that expresses the daily cost C in terms of the number of miles driven, m. (3 points)
C = 0.15m + 20
7. Find the x-intercepts of the graph of y = x^2 - 4x + 3. (3 points)
Set y to zero and solve for x:
x^2 - 4x + 3 = 0
(x - 1)(x - 3) = 0
x = 1 or x = 3
The x-intercepts are (1, 0) and (3, 0).