Final answer:
To find the actual dimensions of a field from a scale drawing, you can use the scale factor of 3.5 feet per inch, so the equation is y = 3.5x, where x is the measurement in inches on the scale drawing and y is the measurement in actual feet.
Step-by-step explanation:
To find the equation that converts the dimensions of a scale drawing to the actual dimensions of a rectangular playing field with a scale of 2 inches equals 7 feet, we use the ratio 2 inches : 7 feet. To express it as an equation in the form of y = kx, where x is a dimension of the scale drawing (in inches) and y is the corresponding dimension of the actual field (in feet), first, we find the conversion factor k which is 7 feet / 2 inches, or 3.5 feet per inch.
The equation representing the relationship between the dimensions on the drawing and the actual dimensions is therefore y = 3.5x.
For example, if the dimension on the drawing is 8 inches, the actual dimension would be y = 3.5 × 8, which equals 28 feet.