Since the line passes through the origin, the equation will be in the form y=mx. To find the slope (m) of the line, we can use the points (3,3) and (8,8) on the line.
m = (8-3)/(8-3)
m = 5/5
m = 1
Therefore, the equation of the line in the form y=mx is y=x.
So, the answer is D. y=x.
Use the image to answer the question.
An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line line passes through points plotted at left parenthesis 3 comma 3 right parenthesis and left parenthesis 8 comma 8 right parenthesis.
Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed.
A. y=3/3x
B. y=8x
C. y=3x
D. y=x
11 answers
Use the image to answer the question.
An illustration shows a graph labeled Inches per Feet. The horizontal axis is labeled feet and ranges from 0 to 4 in increments of 1. The vertical axis is labeled Inches and ranges from 0 to 40 in increments of 4. An upward slanting line segment connects points plotted at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 12 right parenthesis, left parenthesis 2 comma 24 right parenthesis, and left parenthesis 3 comma 36 right parenthesis.
The proportional relationship between inches and feet is displayed on the graph. Derive the equation of the line through the origin.
A. y=2x
B. y=1/12x
C. y=36x
D. y=12x
An illustration shows a graph labeled Inches per Feet. The horizontal axis is labeled feet and ranges from 0 to 4 in increments of 1. The vertical axis is labeled Inches and ranges from 0 to 40 in increments of 4. An upward slanting line segment connects points plotted at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 12 right parenthesis, left parenthesis 2 comma 24 right parenthesis, and left parenthesis 3 comma 36 right parenthesis.
The proportional relationship between inches and feet is displayed on the graph. Derive the equation of the line through the origin.
A. y=2x
B. y=1/12x
C. y=36x
D. y=12x
To find the equation of the line through the origin, we need to calculate the slope (m) using two points on the line. Let's use the points (0,0) and (3,36).
m = (36-0)/(3-0)
m = 36/3
m = 12
Therefore, the equation of the line in the form y=mx is y=12x.
So, the answer is D. y=12x.
m = (36-0)/(3-0)
m = 36/3
m = 12
Therefore, the equation of the line in the form y=mx is y=12x.
So, the answer is D. y=12x.
Use the table to answer the question.
x y (x, y)
0 (0, )
1 (1, )
2 (2, )
Complete the ordered pairs in the table by finding the y-value of the ordered pairs for the equation y=5x .
A. (0, 0), (1, 15) , (2, 25)
B. (0, 0), (5, 1), (10, 2)
C. (0, 0), (1, 5), (3, 15)
D. (0, 0), (1, 5), (2, 10)
x y (x, y)
0 (0, )
1 (1, )
2 (2, )
Complete the ordered pairs in the table by finding the y-value of the ordered pairs for the equation y=5x .
A. (0, 0), (1, 15) , (2, 25)
B. (0, 0), (5, 1), (10, 2)
C. (0, 0), (1, 5), (3, 15)
D. (0, 0), (1, 5), (2, 10)
To find the y-values for the ordered pairs in the table using the equation y=5x, we can simply substitute the x-values into the equation.
For x = 0:
y = 5*0
y = 0
So, the ordered pair is (0, 0).
For x = 1:
y = 5*1
y = 5
So, the ordered pair is (1, 5).
For x = 2:
y = 5*2
y = 10
So, the ordered pair is (2, 10).
Therefore, the completed ordered pairs in the table are (0, 0), (1, 5), and (2, 10).
The correct option is D. (0, 0), (1, 5), (2, 10).
For x = 0:
y = 5*0
y = 0
So, the ordered pair is (0, 0).
For x = 1:
y = 5*1
y = 5
So, the ordered pair is (1, 5).
For x = 2:
y = 5*2
y = 10
So, the ordered pair is (2, 10).
Therefore, the completed ordered pairs in the table are (0, 0), (1, 5), and (2, 10).
The correct option is D. (0, 0), (1, 5), (2, 10).
Graph the proportional relationship y=−2x by plotting points.
A. A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 2 right parenthesis, and left parenthesis 2 comma 4 right parenthesis.
B. A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma negative 1 right parenthesis, and left parenthesis 2 comma negative 2 right parenthesis.
C. A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma negative 2 right parenthesis, and left parenthesis 2 comma negative 4 right parenthesis.
D. A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 5 right parenthesis, and left parenthesis 2 comma 10 right parenthesis.
A. A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 2 right parenthesis, and left parenthesis 2 comma 4 right parenthesis.
B. A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma negative 1 right parenthesis, and left parenthesis 2 comma negative 2 right parenthesis.
C. A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma negative 2 right parenthesis, and left parenthesis 2 comma negative 4 right parenthesis.
D. A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 5 right parenthesis, and left parenthesis 2 comma 10 right parenthesis.
The proportional relationship y=-2x means that for every increase of 1 in x, y decreases by 2.
To graph the equation by plotting points:
- For x = 0, y = -2(0) = 0, giving us the point (0, 0).
- For x = 1, y = -2(1) = -2, giving us the point (1, -2).
- For x = 2, y = -2(2) = -4, giving us the point (2, -4).
The correct option is C. A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: (0, 0), (1, -2), and (2, -4).
To graph the equation by plotting points:
- For x = 0, y = -2(0) = 0, giving us the point (0, 0).
- For x = 1, y = -2(1) = -2, giving us the point (1, -2).
- For x = 2, y = -2(2) = -4, giving us the point (2, -4).
The correct option is C. A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: (0, 0), (1, -2), and (2, -4).
Use the image to answer the question.
A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 5 comma 1 right parenthesis.
Is this the correct graph of the equation y=15x ?
A. No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y=15x
B. Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope m = rise/run = 15.
C. No, it is not the correct graph because the slope m = rise/run = 15.
D. Yes, it is the correct graph because the slope = 51.
A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 5 comma 1 right parenthesis.
Is this the correct graph of the equation y=15x ?
A. No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y=15x
B. Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope m = rise/run = 15.
C. No, it is not the correct graph because the slope m = rise/run = 15.
D. Yes, it is the correct graph because the slope = 51.
To determine if the graph matches the equation y=15x, we need to check if the points (0, 0) and (5, 1) lie on the graph.
When x = 0:
y = 15(0) = 0
So, the point (0, 0) matches the equation.
When x = 5:
y = 15(5) = 75
However, the given point is (5, 1) not (5, 75).
Therefore, the graph is not correct for the equation y=15x because one of the plotted points does not satisfy the equation.
The correct answer is A. No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y=15x.
When x = 0:
y = 15(0) = 0
So, the point (0, 0) matches the equation.
When x = 5:
y = 15(5) = 75
However, the given point is (5, 1) not (5, 75).
Therefore, the graph is not correct for the equation y=15x because one of the plotted points does not satisfy the equation.
The correct answer is A. No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y=15x.
Use the paragraph to answer the question.
The poor horse was very melancholy, and wandered up and down in the wood, seeking some little shelter from the cold wind and rain. Presently a fox met him: "What’s the matter, my friend?" said he. "Why do you hang down your head and look so lonely and woe-begone?" "Ah!" replied the horse, "justice and avarice never dwell in one house; my master has forgotten all that I have done for him so many years, and because I can no longer work he has turned me adrift and says unless I become stronger than a lion he will not take me back again; what chance can I have of that? He knows I have none, or he would not talk so."
Which idea is stated explicitly in the text?
A. The horse believes he has a chance to return to his master.
B. The fox is trying to trick the horse.
C. The horse feels sad about his current situation.
D. The farmer was sad to let his horse go.
The poor horse was very melancholy, and wandered up and down in the wood, seeking some little shelter from the cold wind and rain. Presently a fox met him: "What’s the matter, my friend?" said he. "Why do you hang down your head and look so lonely and woe-begone?" "Ah!" replied the horse, "justice and avarice never dwell in one house; my master has forgotten all that I have done for him so many years, and because I can no longer work he has turned me adrift and says unless I become stronger than a lion he will not take me back again; what chance can I have of that? He knows I have none, or he would not talk so."
Which idea is stated explicitly in the text?
A. The horse believes he has a chance to return to his master.
B. The fox is trying to trick the horse.
C. The horse feels sad about his current situation.
D. The farmer was sad to let his horse go.
The idea stated explicitly in the text is:
C. The horse feels sad about his current situation.
This idea is directly mentioned in the text when the horse is described as very melancholy, seeking shelter from the cold wind and rain, and feeling woe-begone. This indicates that the horse feels sad about his situation.
C. The horse feels sad about his current situation.
This idea is directly mentioned in the text when the horse is described as very melancholy, seeking shelter from the cold wind and rain, and feeling woe-begone. This indicates that the horse feels sad about his situation.
1 answer