Find the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
Since the line passes through the origin, the y-intercept is 0. Therefore, the equation of the line is y = mx + 0 which simplifies to y = mx.
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 = 8x
y = 3x
y = 3/3x
y = x
To find the equation of the line y=mx through the origin, we need to determine the slope of the line. The slope is given by the ratio of the change in the y-coordinate to the change in the x-coordinate for any two points on the line.
Looking at the graph, we can see that for every increase of 1 unit in the x-coordinate, the y-coordinate increases by 1 unit as well. This means that the slope of the line is 1/1, which simplifies to 1.
Therefore, the equation of the line y=mx through the origin is y = 1x. However, the coefficient of 1 is usually omitted in equations, so the simplified equation is y = x.
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.
(1 point)
Responses
y = 36x
y = 2x
y = 12x
y = 1/12x
Since the line passes through the origin, the y-intercept is 0. The slope of the line can be found by picking two points on the line and calculating the change in y divided by the change in x.
Let's pick two points: (0, 0) and (2, 24).
The change in y = 24 - 0 = 24
The change in x = 2 - 0 = 2
So, the slope of the line is 24/2 = 12.
Therefore, the equation of the line y=mx 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
A. (0, 0), (1, 5), (3, 15)
B. (0, 0), (1, 5), (2, 10)
C. (0, 0), (1, 15) , (2, 25)
D. (0, 0), (5, 1), (10, 2)
The equation y = 5x means that for any given value of x, the corresponding y-coordinate is 5 times that value.
Using the given x-values:
For x = 0, y = 5(0) = 0
For x = 1, y = 5(1) = 5
For x = 2, y = 5(2) = 10
Therefore, the correct option is B. (0, 0), (1, 5), (2, 10)
Graph the proportional relationship y = −2x by plotting points.
To graph the proportional relationship y = -2x, we can plot a few points that satisfy this equation.
Let's choose some values for x and find the corresponding y-values:
For x = 0, y = -2(0) = 0. So we have the point (0, 0).
For x = 1, y = -2(1) = -2. So we have the point (1, -2).
For x = 2, y = -2(2) = -4. So we have the point (2, -4).
Now we can plot these points on a graph. The x-coordinate represents the input value (x) and the y-coordinate represents the output value (y).
The graph would look like this:
(0, 0) (1, -2) (2, -4)
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The line passing through the points (0, 0), (1, -2), and (2, -4) represents the proportional relationship y = -2x.