The correct equation for a line through the origin based on the given graph is:
y = x
Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed.
(1 point)
Responses
y=33x
y equals Start Fraction 3 over 3 End Fraction x
y=3x
y equals 3 x
y=8x
y equals 8 x
y=x
9 answers
The proportional relationship between inches and feet is displayed on the graph. Derive the equation of the line through the origin.
(1 point)
Responses
y=36x
y=12x
y=1/12x
y=2x
(1 point)
Responses
y=36x
y=12x
y=1/12x
y=2x
Inches and feet have a proportional relationship, which means that for every 1 foot (x), there are 12 inches (y).
So, the equation for the line through the origin is:
y = 12x
So, the equation for the line through the origin is:
y = 12x
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.
(1 point)
Responses
(0, 0), (1, 5), (2, 10)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 1 comma 5 right parenthesis , left parenthesis 2 comma 10 right parenthesis
(0, 0), (1, 15) , (2, 25)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 1 comma Start Fraction 1 over 5 End Fraction right parenthesis , left parenthesis 2 comma Start Fraction 2 over 5 End Fraction right parenthesis
(0, 0), (5, 1), (10, 2)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 5 comma 1 right parenthesis , left parenthesis 10 comma 2 right parenthesis
(0, 0), (1, 5), (3, 15)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 1 comma 5 right parenthesis , left parenthesis 3 comma 15 right parenthesis
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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.
(1 point)
Responses
(0, 0), (1, 5), (2, 10)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 1 comma 5 right parenthesis , left parenthesis 2 comma 10 right parenthesis
(0, 0), (1, 15) , (2, 25)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 1 comma Start Fraction 1 over 5 End Fraction right parenthesis , left parenthesis 2 comma Start Fraction 2 over 5 End Fraction right parenthesis
(0, 0), (5, 1), (10, 2)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 5 comma 1 right parenthesis , left parenthesis 10 comma 2 right parenthesis
(0, 0), (1, 5), (3, 15)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 1 comma 5 right parenthesis , left parenthesis 3 comma 15 right parenthesis
Skip to navigation
The equation y=5x implies that for every x-value, the corresponding y-value will be 5 times that x-value.
So, completing the ordered pairs in the table:
(0, 0), (1, 5), (2, 10)
So, completing the ordered pairs in the table:
(0, 0), (1, 5), (2, 10)
Graph the proportional relationship y=−2x by plotting points.
To graph the proportional relationship y = -2x, you can plot points using different x-values and their corresponding y-values.
Here are a few points that you can plot to graph the equation:
(x, y) = (0, 0)
(x, y) = (1, -2)
(x, y) = (2, -4)
(x, y) = (-1, 2)
(x, y) = (-2, 4)
Plotting these points on a graph will give you a straight line passing through the origin with a slope of -2, indicating the proportional relationship y = -2x.
Here is a visual representation of the graph:
|
4 | ●
| ● ●
3 |
| ●
2 |
| ●
1 |
|
0 | ●
------------------
-2 -1 0 1 2
x-axis y-axis
Here are a few points that you can plot to graph the equation:
(x, y) = (0, 0)
(x, y) = (1, -2)
(x, y) = (2, -4)
(x, y) = (-1, 2)
(x, y) = (-2, 4)
Plotting these points on a graph will give you a straight line passing through the origin with a slope of -2, indicating the proportional relationship y = -2x.
Here is a visual representation of the graph:
|
4 | ●
| ● ●
3 |
| ●
2 |
| ●
1 |
|
0 | ●
------------------
-2 -1 0 1 2
x-axis y-axis
Graphing Proportional Relationships Quick Check
5 of 55 of 5 Items
Question
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?
(1 point)
Responses
No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y=15x
No, it is not the correct graph because the ordered pair left parenthesis 1 comma 5 right parenthesis is not a point on the graph of y equals Start Fraction 1 over 5 End Fraction x
No, it is not the correct graph because the slope m=riserun=15.
No, it is not the correct graph because the slope m equals Start Fraction rise over run End Fraction equals Start Fraction 1 over 5 End Fraction .
Yes, it is the correct graph because the slope =51.
Yes, it is the correct graph because the slope equals Start Fraction 5 over 1 End Fraction .
Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope m=riserun=15.
5 of 55 of 5 Items
Question
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?
(1 point)
Responses
No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y=15x
No, it is not the correct graph because the ordered pair left parenthesis 1 comma 5 right parenthesis is not a point on the graph of y equals Start Fraction 1 over 5 End Fraction x
No, it is not the correct graph because the slope m=riserun=15.
No, it is not the correct graph because the slope m equals Start Fraction rise over run End Fraction equals Start Fraction 1 over 5 End Fraction .
Yes, it is the correct graph because the slope =51.
Yes, it is the correct graph because the slope equals Start Fraction 5 over 1 End Fraction .
Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope m=riserun=15.
No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y = 15x.