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.

Answer 1

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.