Which ordered pair is a solution of the equation y = 3x?
Responses
(–2, –9)
(–2, –9)
(–8, –18)
(–8, –18)
(–8, –3)
(–8, –3)
(–10, –30)
To determine if an ordered pair is a solution of the equation y = 3x, substitute the x and y values into the equation and check if both sides are equal.
Let's try the first ordered pair, (-2, -9)
Substitute x = -2 and y = -9 into the equation:
-9 = 3(-2)
This equation simplifies to:
-9 = -6
Since -9 is not equal to -6, the first ordered pair, (-2, -9), is not a solution of the equation y = 3x.
Now, let's try the second ordered pair, (-8, -18)
Substitute x = -8 and y = -18 into the equation:
-18 = 3(-8)
This equation simplifies to:
-18 = -24
Since -18 is not equal to -24, the second ordered pair, (-8, -18), is not a solution of the equation y = 3x.
Next, let's try the third ordered pair, (-8, -3)
Substitute x = -8 and y = -3 into the equation:
-3 = 3(-8)
This equation simplifies to:
-3 = -24
Since -3 is not equal to -24, the third ordered pair, (-8, -3), is not a solution of the equation y = 3x.
Finally, let's try the fourth ordered pair, (-10, -30)
Substitute x = -10 and y = -30 into the equation:
-30 = 3(-10)
This equation simplifies to:
-30 = -30
Since -30 is equal to -30, the fourth ordered pair, (-10, -30), is a solution of the equation y = 3x.
Therefore, the ordered pair (-10, -30) is a solution of the equation y = 3x.
Which ordered pair is a solution of the equation y = –7x + 2?
Responses
(1, 2)
(1, 2)
(8, –54)
(8, –54)
(5, –35)
(5, –35)
(1, –7)
(1, –7)
To determine if an ordered pair is a solution of the equation y = -7x + 2, substitute the x and y values into the equation and check if both sides are equal.
Let's try the first ordered pair, (1, 2).
Substitute x = 1 and y = 2 into the equation:
2 = -7(1) + 2
Simplifying the equation:
2 = -7 + 2
This equation simplifies to:
2 = -5
Since 2 is not equal to -5, the first ordered pair, (1, 2), is not a solution of the equation y = -7x + 2.
Let's try the second ordered pair, (8, -54).
Substitute x = 8 and y = -54 into the equation:
-54 = -7(8) + 2
Simplifying the equation:
-54 = -56 + 2
This equation simplifies to:
-54 = -54
Since -54 is equal to -54, the second ordered pair, (8, -54), is a solution of the equation y = -7x + 2.
Let's try the third ordered pair, (5, -35).
Substitute x = 5 and y = -35 into the equation:
-35 = -7(5) + 2
Simplifying the equation:
-35 = -35 + 2
This equation simplifies to:
-35 = -33
Since -35 is not equal to -33, the third ordered pair, (5, -35), is not a solution of the equation y = -7x + 2.
Finally, let's try the fourth ordered pair, (1, -7).
Substitute x = 1 and y = -7 into the equation:
-7 = -7(1) + 2
Simplifying the equation:
-7 = -7 + 2
This equation simplifies to:
-7 = -5
Since -7 is not equal to -5, the fourth ordered pair, (1, -7), is not a solution of the equation y = -7x + 2.
Therefore, the only ordered pair that is a solution of the equation y = -7x + 2 is (8, -54).
Nick and his cousin Sara have the same birthday, but Nick is four years older than Sara. Let the variable x represent Nick’s age and y represent Sara’s age. Which graph represents the relationship between Nick’s age and Sara’s age?
(1 point)
Responses
The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages.The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 0 comma 4 right parenthesis, left parenthesis 2 comma 6 right parenthesis, and left parenthesis 4 comma 8 right parenthesis.
Image with alt text: The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 0 comma 4 right parenthesis, left parenthesis 2 comma 6 right parenthesis, and left parenthesis 4 comma 8 right parenthesis.
The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages.The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 0 comma 0 right parenthesis, left parenthesis 4 comma one-half right parenthesis, and left parenthesis 8 comma 1 right parenthesis.
Image with alt text: The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 0 comma 0 right parenthesis, left parenthesis 4 comma one-half right parenthesis, and left parenthesis 8 comma 1 right parenthesis.
The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages.The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left-parenthesis 0 comma 0 right-parenthesis, left-parenthesis one-half comma 4 right-parenthesis, and left-parenthesis 1 comma 8 right-parenthesis.
Image with alt text: The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left-parenthesis 0 comma 0 right-parenthesis, left-parenthesis one-half comma 4 right-parenthesis, and left-parenthesis 1 comma 8 right-parenthesis.
The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages.The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 4 comma 0 right parenthesis, left parenthesis 6 comma 2 right parenthesis, and left parenthesis 8 comma 4 right parenthesis.
Image with alt text: The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points left parenthesis 4 comma 0 right parenthesis, left parenthesis 6 comma 2 right parenthesis, and left parenthesis 8 comma 4 right parenthesis.
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The correct graph that represents the relationship between Nick's age and Sara's age is:
The first quadrant of a coordinate plane titled Nick’s and Sara’s Ages. The x-axis is labeled Nick’s Age in years. The y-axis is labeled Sara’s Age in years. The graph shows a line passing through the points (0, 4), (2, 6), and (4, 8).
Solve the following equation.
–4 = g + 1
(1 point)
Responses
g = –4
g = –4
g = 4
g = 4
g = –5
g = –5
g = –3
To solve the equation -4 = g + 1, you can isolate the variable g.
Start by subtracting 1 from both sides of the equation:
-4 - 1 = g + 1 - 1
-5 = g
So, the solution to the equation is:
g = -5
Solve the following equation.
w – 2 = –3
(1 point)
Responses
w = negative three-halves
w = Image with alt text: negative three-halves
w = –5
w = –5
w = –1
w = –1
w = 6
To solve the equation w - 2 = -3, you can isolate the variable w.
Start by adding 2 to both sides of the equation:
w - 2 + 2 = -3 + 2
w = -1
So, the solution to the equation is:
w = -1
Solve the following equation.
6.4 = 4x
(1 point)
Responses
x = 2.4
x = 2.4
x = 1.6
x = 1.6
x = 4
x = 4
x = 6.4