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=1/12x
y equals Start Fraction 1 over 12 End Fraction x
y=36x
y equals 36 x
y=12x
y equals 12 x
y=2x
y = 1/12x is the correct equation for the line through the origin that represents the proportional relationship between inches and feet.
To derive the equation of the line through the origin, we need to find the slope of the line and the y-intercept.
The proportional relationship between inches and feet implies that for every 12 inches, there is 1 foot. This means that the slope of the line can be calculated as the change in y divided by the change in x.
Given that the y-axis represents feet and the x-axis represents inches, the change in y is 1 foot and the change in x is 12 inches. Thus, the slope of the line is 1/12.
Since the line passes through the origin, the y-intercept is 0.
Putting these pieces together, we can form the equation of the line by using the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Therefore, the equation of the line through the origin is y = (1/12)x.
Alternatively, you can also express this as y = 1/12x or y equals Start Fraction 1 over 12 End Fraction x. All three of these notations are equivalent and valid representations of the equation.
In this case, the proportional relationship between inches and feet is displayed on the graph as a straight line passing through the origin. To derive the equation of this line, we can look at the slope of the line.
The slope of a line represents the rate of change between the y-values (feet) and x-values (inches). In this case, for every 12 inches (1 foot), the y-value increases by 1 foot.
Therefore, the equation of the line through the origin is:
y = 1/12x
or
y = (1/12)x