Question

in 1970, a music store sold 350 CDs per day. In 1985, they sold 275 CDs per day. Let x represent the number of years since 1990. Assuming a linear relationship, what is an equation to model this scenario?

Answer 1

Given in the question:

a.) In 1970, a music store sold 350 CDs per day.

b.) In 1985, they sold 275 CDs per day.

Step 1: Let's transform the given into ordered pairs. Let x represent the number of years since 1990.

a.) In 1970, a music store sold 350 CDs per day. = x1,y1 = 1970 - 1990,350 = -20,350

b.) In 1985, they sold 275 CDs per day. = x2,y22 = 1985-1990,275 = -5,275

Step 2: Let's use the slope-intercept formula in making the equation of the scenario.

a.) The slope of the line (m).

`\text{ m = }\frac{y_2-y_{1_{}}}{x_2-x_1}`
`\text{ m = }\frac{275\text{ - 350}}{-5-(-20)}\text{ = }\frac{-75}{-5\text{ + }20}\text{ = }(-75)/(15)\text{ = -5}`
`\text{ m = -}5`

b.) The y-intercept (b). Substitute m = -5 and x,y= -20,350 in the y = mx + b.

`\text{ y = mx + b}`
`350\text{ = (-5})(-20)\text{ + b}`
`\text{350 = }100\text{ + b}`
`\text{ b = 3}50\text{ - 100}`
`\text{ b = 2}50`

Step 3: Let's complete the equation. Substitute m = -5 and b = 250.

`\text{ y = mx + b}`
`\text{ y = (-}5)x\text{ + (250})`
`\text{ y =- }5x\text{ + 2}50`

Therefore, the equation to model this scenario is y = -5x + 250.