The ordered pairs (2, –11) and (5, –20) are solutions to which of the following equations?
A. y = 3x – 5
B. y = –3x + 5
C. y = 3x + 5
D. y = –3x – 5
D. y = –3x – 5
Which is a rule that describes the translation of a point from (–5, 4) to (–1, 2)?
A. (x, y) arrow(x – 4, y – 2)
B. (x, y) arrow(x + 4, y – 2)
C. (x, y) arrow(x + 4, y + 2)
D. (x, y) arrow(x – 4, y + 2)
B. (x, y) arrow(x + 4, y – 2)
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’?
A. J' (15, 9), K' (12, 7), L' (9, 13)
B. J' (15, 9), K' (7, 12), L' (9, 13)
C. J' (14, 10), K' (6, 13), L' (10, 12)
D. J' (15, 5), K' (7, 8), L' (9, 9)
A. J' (15, 9), K' (12, 7), L' (9, 13)
A transformation translates the point upper S left-parenthesis negative 1 comma 1 right-parenthesisdown 2 units and right 3 units. What rule describes this translation?
A. left-parenthesis x comma y right-parenthesis right-arrow left-parenthesis x minus 2 comma y plus 3 right-parenthesis
B. left-parenthesis x comma y right-parenthesis right-arrow left-parenthesis x plus 2 comma y minus 3 right-parenthesis
C. left-parenthesis x comma y right-parenthesis right-arrow left-parenthesis x minus 3 comma y plus 2 right-parenthesis
D. left-parenthesis x comma y right-parenthesis right-arrow left-parenthesis x plus 3 comma y minus 2 right-parenthesis
D. (x, y) → (x + 3, y - 2)
The coordinates of two vertices of a right triangle are shown on the grid.
A coordinate graph with x and y axes labeled from negative 5 to 5 is shown. A dot at the point left parenthesis negative 2 comma 5 right parenthesis is labeled A and the left parenthesis point five comma negative 3 right parenthesis is labeled B. A line segment connects the points.
Which could be the coordinates of the right triangle's third vertex?
A. (–2, –3)
B. (–2, 3)
C. (2, 3)
d. (2, -3
A. (–2, –3)
Which graph shows the image of a figure after a rotation of 180° around the origin?
A. graph AThe coordinates of the vertices for the first square are upper A superscript 1 baseline left-parenthesis negative 2 comma 3 right-parenthesis, upper B superscript 1 baseline left-parenthesis negative 3 comma 1 right-parenthesis, upper C superscript 1 baseline left-parenthesis negative 1 comma 0 right-parenthesis, and upper D superscript 1 baseline left-parenthesis 2 comma 0 right-parenthesis. The coordinates of the vertices for the second square are upper A left-parenthesis 2 comma 3 right-parenthesis, upper B left-parenthesis 3 comma 1 right-parenthesis, upper C left-parenthesis 1 comma 0 right-parenthesis, and upper D left-parenthesis 2 comma 0 right-parenthesis.
B. graph BThe coordinates of the vertices for the first square are upper A superscript 1 baseline left-parenthesis negative 2 comma 3 right-parenthesis, upper B superscript 1 baseline left-parenthesis negative 3 comma 1 right-parenthesis, upper C superscript 1 baseline left-parenthesis negative 1 comma 0 right-parenthesis, and upper D superscript 1 baseline left-parenthesis 2 comma 0 right-parenthesis. The coordinates of the vertices for the second square are upper A left-parenthesis negative 2 comma 3 right-parenthesis, upper B left-parenthesis 1 comma negative 1 right-parenthesis, upper C left-parenthesis 1 comma 0 right-parenthesis, and upper D left-parenthesis 0 comma negative 2 right-parenthesis.
C. graph CThe coordinates of the vertices for the first square are upper A superscript 1 baseline left-parenthesis negative 2 comma 3 right-parenthesis, upper B superscript 1 baseline left-parenthesis negative 3 comma 1 right-parenthesis, upper C superscript 1 baseline left-parenthesis negative 1 comma 0 right-parenthesis, and upper D superscript 1 baseline left-parenthesis 2 comma 0 right-parenthesis. The coordinates of the vertices for the second square are upper A left-parenthesis negative 5 comma negative 2 right-parenthesis, upper B left-parenthesis negative 4 comma negative 4 right-parenthesis, upper C left-parenthesis negative 2 comma negative 3 right-parenthesis, and upper D left-parenthesis negative 3 comma negative 1 right-parenthesis.
D. graph DThe coordinates of the vertices for the first square are upper A superscript 1 baseline left-parenthesis negative 2 comma 3 right-parenthesis, upper B superscript 1 baseline left-parenthesis negative 3 comma 1 right-parenthesis, upper C superscript 1 baseline left-parenthesis negative 1 comma 0 right-parenthesis, and upper D superscript 1 baseline left-parenthesis 2 comma 0 right-parenthesis. The coordinates of the vertices for the second square are upper A left-parenthesis negative 2 comma negative 3 right-parenthesis, upper B left-parenthesis 1 comma negative 4 right-parenthesis, upper C left-parenthesis 2 comma negative 1 right-parenthesis, and upper D left-parenthesis negative 1 comma 0 right-parenthesis.
D. graph D
Which table shows a proportional relationship?
A. table aIn column 1, x is 1 and y is 2.
In column 2, x is 3 and y is 4.
In column 3, x is 4 and y is 6.
In column 4, x is 6 and y is 7.
B. table bIn column 1, x is 1 and y is negative 2. In column 2, x is 2 and y is 0. In column 3, x is 5 and y is 6. In column 4, x is 8 and y is 12.
C. table cIn column 1, x is 2 and y is negative 4.
In column 2, x is 3 and y is negative 6.
In column 3, x is 5 and y is negative 10.
In column 4, x is 6 and y is negative 12.
D. table DIn column 1, x is 2 and y is 2.
In column 2, x is 4 and y is 3.
In column 3, x is 6 and y is 4.
In column 4, x is 8 and y is 5.
A. table a
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.
A. 15 gallons per mile
B. 8 miles per gallon
C. 15 miles per gallon
D. 8 gallons per mile
D. 8 gallons per mile
The graph below shows Cara's earnings according to the number of hours she works.
A coordinate graph is shown.
The graph has an x axis labeled 'Number of Hours Worked' with coordinates labeled from 0 to 40 in multiples of 5. The y axis is labeled 'Number of Dollars Earned' and is marked from 0 to 400 in multiples of 100. A red ray on the graph begins at 0 comma 0 and extends up and to the right through the point 35 comma 350.
What does the slope of the line represent?
A. For every $50 Cara earns, she works 10 hours.
B. For every $50 Cara earns, she works 3 hours.
C. For each hour Cara works, she earns $10.
D. For each hour Cara works, she earns $15.
C. For each hour Cara works, she earns $10.
Which of the following is a graph of y = x2?
A. 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.
B. 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.
C. 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.
D. 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.
A. 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.
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?
A. A = 7.50h
B. A = 22.50h
C. A = h + 7.50
D. A = h + 22.50
A. A = 7.50h
Short Answer
Note: For questions 19 and 20, your teacher will grade your response to ensure you receive proper credit for your answer.
Point A(4, 2) is translated according to the rule (x, y) right arrow (x + 1, y – 5) and then reflected across the y-axis.
a) In which quadrant of the coordinate plane is point A located?
b) What are the coordinates of translated point A’? In which quadrant of the coordinate plane is point A’ located?
c) What are the coordinates of reflected point A’’? In which quadrant of the coordinate plane is point A’’ located?
a) Point A is located in Quadrant I.
b) Applying the translation rule, we have A' = (4+1, 2-5) = (5, -3). Point A' is located in Quadrant IV.
c) Reflecting A' across the y-axis, we change the x-coordinate to its opposite value, giving us A'' = (-5, -3). Point A'' is located in Quadrant III.