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=112x
y equals Start Fraction 1 over 12 End Fraction x
y=36x
y equals 36 x
y=2x
y=1/12x
To derive the equation of the line through the origin that represents the proportional relationship between inches and feet, we need to determine the slope of the line using the given information on the graph.
The slope of a line represents the rate of change between the variables in the relationship. In this case, the slope of the line represents the number of inches for every foot (or how many inches we have for each unit increase in feet).
From the graph, we can see that as the x-coordinate (feet) increases by 1, the y-coordinate (inches) increases by 12. This means that for every 1 foot increase, there is a corresponding 12-inch increase.
Using the slope-intercept form of a linear equation (y = mx + b), where m represents the slope and b represents the y-intercept (which is 0 in this case as the line passes through the origin), we can substitute the slope value:
m = 12
Therefore, the equation of the line through the origin representing the proportional relationship between inches and feet is:
y = 12x