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
The correct equation for a line through the origin based on the given graph is:
y = x
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
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
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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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)
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
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.
No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y = 15x.
To derive the equation y=mx for a line through the origin using a graph, we need to find the slope of the line. The slope is the ratio of the vertical change to the horizontal change between any two points on the line.
In this case, since the line passes through the origin, we can take any point on the line and the origin itself to calculate the slope. Let's choose the point (1, y) on the line.
The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
We know that one point is (1, y), and the other point is the origin (0, 0). Substituting these values into the slope formula, we get:
m = (y - 0) / (1 - 0)
m = y
So the slope (m) is y.
Therefore, the equation of the line through the origin is y = mx. In this case, the simplified numerical coefficient is 1, which means the equation can be written as y = x.
Hence, the correct equation is y = x.