Write the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
(1,3), (2,6), (3,9)
The graph represents the proportional relationship between inches and feet. To derive the equation of the line, we need to determine the slope of the line. Since the relationship is proportional, the slope should be constant.
From the graph, we can see that for every increase of 1 inch, there is a corresponding increase of 1/12 feet. This informs us that the slope (m) of the line is equal to 1/12.
Therefore, the equation of the line through the origin is y = (1/12)x or y = 1/12x.
write the equation of line y=mx through the origin that describes the proportional relationship shown in the graph
use the image to answer the question
Write the equation of the line y=Mx through the origin that describes the proportional relationship shown in the graph
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=x
y equals x
y=8x
y equals 8 x
y=3x
The graph shows a straight line passing through the origin, indicating a proportional relationship. The slope of this line can be determined by considering the ratio of the y-coordinate to the x-coordinate of any point on the line.
Looking at the points on the graph, we can see that for every increase of 1 in x, there is a corresponding 3-unit increase in y. This means the slope (m) of the line is 3.
Therefore, the equation of the line is y = 3x.
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=2x
y equals 2 x
y=112x
y equals Start Fraction 1 over 12 End Fraction x
y=36x
y equals 36 x
y=12x
To find the slope (m) of the line, we can use the formula:
m = (change in y) / (change in x)
Using the points (1,3) and (3,9), we have:
change in y = 9 - 3 = 6
change in x = 3 - 1 = 2
So the slope is m = 6/2 = 3.
Since the line passes through the origin, the y-intercept (b) is 0.
Therefore, the equation of the line is y = 3x.