Question
Inches per feet y=12,1 y=24,1 y=36,3. The proportional relationship between inches and feet is displayed on the graph. Derive the equation of the line through the origin.
Answers
GPT 3.5
To derive the equation of the line through the origin, we need to determine the slope of the line.
The slope of a line can be found using the formula: slope = (change in y) / (change in x)
From the given data points:
- The change in x (inches) is always 12 because 12 inches make 1 foot.
- The change in y (feet) is given as follows:
- From y=12,1 to y=24,1, the change in y is 24 - 12 = 12.
- From y=24,1 to y=36,3, the change in y is 36 - 24 = 12.
Thus, the slope of the line is: slope = (12) / (12) = 1.
The equation of a line through the origin is y = mx, where m is the slope. Therefore, the equation of the line is y = 1x, or simply y = x.
The slope of a line can be found using the formula: slope = (change in y) / (change in x)
From the given data points:
- The change in x (inches) is always 12 because 12 inches make 1 foot.
- The change in y (feet) is given as follows:
- From y=12,1 to y=24,1, the change in y is 24 - 12 = 12.
- From y=24,1 to y=36,3, the change in y is 36 - 24 = 12.
Thus, the slope of the line is: slope = (12) / (12) = 1.
The equation of a line through the origin is y = mx, where m is the slope. Therefore, the equation of the line is y = 1x, or simply y = x.