Question

zoe starts with 15 dollars in her account. she earns 10 dollars per hour babysitting and deposits the earnings into her account. chloe starts with -20 dollars in her account. she earns 10 dollars per hour babysitting and deposits the earnings into her account. both lines have a slope of 10. what does that mean in this situation? zoe: d = 15 + 10x the slope of zoes line is 10. chloe: d = -20 + 10x the slope of chloes line is 10. zoe always has $10 more in her account than chloe. they both started with $10 in their accounts. they both earn $10 per hour.

Explanation:

Step1: Recall slope meaning in linear equations

In a linear equation \( y = mx + b \), \( m \) (slope) represents the rate of change of \( y \) with respect to \( x \). Here, the equations are \( d = 15 + 10x \) (Zoe) and \( d = -20 + 10x \) (Chloe), where \( d \) is dollars in account, \( x \) is hours.

Step2: Analyze each option

• First option: Zoe's start is \( 15 \), Chloe's is \( -20 \), difference is \( 35 \), not always \( 10 \).
• Second option: Zoe started with \( 15 \), Chloe with \( -20 \), not \( 10 \).
• Third option: Slope \( 10 \) means for each hour (\( x \) increases by 1), \( d \) (dollars) increases by 10, so they earn $10 per hour.

Answer:

They both earn $10 per hour.