Science

A spring stretches in relation to the weight hanging from it according to the equation \(\text{y} = 0.75\text{x} + 0.25\) where x is the weight in pounds and y is the length of the spring in inches.

a. Graph the equation. Include axis labels.

b. Interpret the slope and the y-intercept of the line.

c. How long will the spring be if a 2-pound weight is hung on it? Will the length double if you double the weight? Explain

slope = 5, y-intercept = -1

slope = -1, y-intercept = 8

slope = 0.2, y-intercept = 0.3

slope = 1.5, y-intercept = -3

slope = \(- \large\frac{1}{2}\), y-intercept = 4

slope = \(\large\frac{2}{3}\), y-intercept = -5

A music school charges a registration fee in addition to a fee per lesson. Music lessons last 0.5 hour. The equation \(\text{y} = 40\text{x} + 30\) represents the total cost y of x lessons. Find and interpret the slope and y-intercept of the line that represents this situation. Then find four points on the line.