Question

1. as a clock salesperson at the time store, owen helps customers pick out the right clock for their needs. he earns a commission on each clock he sells. there is a proportional relationship between the price (in dollars) of a clock owen sells, x, and the commission (in dollars) he earns, y. x (dollars in sales) | y (dollars in commission) $25 $2 $50 $4 $75 $6 $100 $8 write an equation for the relationship between x and y. simplify any fractions. y = 7. bella is participating in a fun run to raise money for the west side childrens hospital. the run is held at bellas high school track. the more laps bella runs around the track, the more money she raises for the hospital. there is a proportional relationship between the number of laps bella runs, x, and the amount of money she raises for the hospital (in dollars), y. x (laps) | y (dollars) 2 $22 6 $66 7 $77 8 $88 write an equation for the relationship between x and y. simplify any fractions. y =

Explanation:

Problem 6

Step1: Recall proportional relationship formula

For a proportional relationship, the equation is \( y = kx \), where \( k \) is the constant of proportionality. To find \( k \), we can use the formula \( k=\frac{y}{x} \).
Take the first pair of values from the table: \( x = 25 \), \( y = 2 \). Then \( k=\frac{2}{25} \). Let's check with another pair, say \( x = 50 \), \( y = 4 \). \( \frac{4}{50}=\frac{2}{25} \), which is the same. So \( k=\frac{2}{25} \).

Step2: Write the equation

Substitute \( k = \frac{2}{25} \) into \( y=kx \). So the equation is \( y=\frac{2}{25}x \).

Step1: Recall proportional relationship formula

For a proportional relationship, \( y = kx \), and \( k=\frac{y}{x} \).
Take the first pair: \( x = 2 \), \( y = 22 \). Then \( k=\frac{22}{2}=11 \). Check with another pair, \( x = 6 \), \( y = 66 \). \( \frac{66}{6}=11 \), which matches. So \( k = 11 \).

Step2: Write the equation

Substitute \( k = 11 \) into \( y=kx \). So the equation is \( y = 11x \).

Answer:

\( y = \frac{2}{25}x \)

Problem 7