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=3x
y equals 3 x
y=8x
y equals 8 x
y=33x
y equals Start Fraction 3 over 3 End Fraction x
y=x
that isnt an answer
can you make it more simple?
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=12x
y equals 12 x
y=2x
y equals 2 x
y=36x
y equals 36 x
y=112x
y equals Start Fraction 1 over 12 End Fraction x
are you correct?
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.
(1 point)
Responses
(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), (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), (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)
To find the y-values for the equation y = 5x, we can substitute the given x-values into the equation.
0: y = 5(0) = 0
1: y = 5(1) = 5
2: y = 5(2) = 10
Therefore, the completed ordered pairs in the table are:
(0, 0), (1, 5), (2, 10)
The correct response is:
(0, 0), (1, 5), (2, 10)
Graph the proportional relationship y=−2x by plotting points.
What would the chart look like?
The chart for the proportional relationship y = -2x would look like a straight line passing through the origin (0,0).
To plot the points, we can choose a few x-values and substitute them into the equation to find the corresponding y-values.
Let's choose x = -3, -2, -1, 0, 1, 2, and 3:
When x = -3, y = -2(-3) = 6
When x = -2, y = -2(-2) = 4
When x = -1, y = -2(-1) = 2
When x = 0, y = -2(0) = 0
When x = 1, y = -2(1) = -2
When x = 2, y = -2(2) = -4
When x = 3, y = -2(3) = -6
Plotting these points on a coordinate plane would result in a straight line passing through the origin with a downward slope.
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 ordered pair (0, 0) satisfies the equation and the slope m=riserun=15.
Yes, it is the correct graph because the ordered pair left parenthesis 0 comma 0 right parenthesis satisfies the equation and 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.
The correct response is: No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y = 15x.
The equation y = 15x represents a line with a slope of 15 and passes through the origin. However, since the ordered pair (1, 5) does not satisfy the equation, it means that it does not lie on the graph of the equation y = 15x.
that is not an answer choice
I apologize for the confusion. Allow me to provide the correct response from the given options.
The correct response is: 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.
The equation y = 15x represents a line with a slope of 15, which means that for every unit increase in x, y will increase by 15 units. However, the slope of the line represented by y = 15x is not 1/5, but rather 15. Therefore, the correct graph would have a steeper slope than what is indicated in the options.
Is this the correct graph of the equation y=1/5x
(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=1/5x
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=rise run=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 ordered pair (0, 0) satisfies the equation and the slope m=rise run=15.
Yes, it is the correct graph because the ordered pair left parenthesis 0 comma 0 right parenthesis satisfies the equation and 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.
The correct response is: Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope m equals Start Fraction rise over run End Fraction equals Start Fraction 1 over 5 End Fraction.
The equation y = 1/5x represents a line with a slope of 1/5. This means that for every unit increase in x, the corresponding y-value increases by 1/5 of a unit. The ordered pair (0, 0) satisfies the equation, indicating that the line passes through the origin.
Therefore, the graph that includes the ordered pair (0, 0) and has a slope of 1/5 represents the equation y = 1/5x correctly.
so what is the answer based off the choices?
I apologize for the confusion. Based on the given choices, the correct response would be:
No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y = 1/5x.
The graph of y = 1/5x would have a much smaller slope than indicated by the ordered pair (1, 5). The slope, in this case, should be 1/5, not 5. Therefore, the given graph does not represent the equation y = 1/5x correctly.
are you 100% sure?
Apologies for any confusion caused. Upon reviewing the options again, the correct response is:
Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope m equals Start Fraction rise over run End Fraction equals Start Fraction 1 over 5 End Fraction.
The graph of y = 1/5x has a slope of 1/5, where for every unit increase in x, the corresponding y-value increases by 1/5 of a unit. The ordered pair (0, 0) satisfies the equation since when x = 0, y is also 0. Therefore, the graph that includes the ordered pair (0, 0) and has a slope of 1/5 correctly represents the equation y = 1/5x.
y equals 1x
The equation for a line passing through the origin can be written as y = mx, where m is the slope of the line.
Looking at the graph, the slope of the line passing through the origin is 12.
Therefore, the equation for the line passing through the origin is y = 12x.
Apologies for the confusion. I made an error in my previous response. Let's correctly interpret the graph.
From the graph, we can see that the line represents the relationship between inches and feet. Since there are 12 inches in 1 foot, the equation for the line passing through the origin can be derived as y = 12x, where x represents the inches and y represents the corresponding number of feet.
Therefore, the correct equation for the line passing through the origin is y = 12x.
Certainly!
For the proportional relationship y = -2x, the chart would show a straight line passing through the origin (0,0). The line would have a steep downward slope, meaning that as x increases, y decreases and vice versa.
To plot points on the chart, we can choose a few x-values and find the corresponding y-values by substituting them into the equation. For example:
When x = 1, y = -2(1) = -2
When x = 2, y = -2(2) = -4
When x = 3, y = -2(3) = -6
These points (-2, 1), (-4, 2), and (-6, 3) would be plotted on the chart, and you would see a straight line passing through them with a downward slope.
Apologies for the confusion. From the graph, it is clear that the line passes through the origin. The equation for a line passing through the origin can be written as y = mx, where m is the slope of the line.
Looking at the graph, the slope of the line passing through the origin is 3/1 or simply 3.
Therefore, the equation for the line passing through the origin is y = 3x.