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. what do the vertical intercepts mean in this situation? zoe: d = 15 + 10x the slope of zoes line is 10. the vertical intercept of zoes line is 15. chloe: d = -20 + 10x the slope of chloes line is 10. the vertical intercept of chloes line is -20. zoe started with $15 in her account and chloe started with -$20 in her account. zoe earns $15 per hour and chloe earns -$20 per hour. zoe always has 15 times as much money as chloe.

Explanation:

Step1: Recall vertical intercept meaning

In a linear equation \( y = mx + b \), the vertical intercept (\( b \)) is the value of \( y \) when \( x = 0 \). Here, \( x \) is hours babysitting, \( d \) (dollars in account) is \( y \).

Step2: Analyze Zoe's equation

Zoe's equation: \( d = 15 + 10x \). When \( x = 0 \) (0 hours babysitting), \( d = 15 \). So vertical intercept 15 means her starting account balance.

Step3: Analyze Chloe's equation

Chloe's equation: \( d = -20 + 10x \). When \( x = 0 \) (0 hours babysitting), \( d = -20 \). So vertical intercept -20 means her starting account balance.

Step4: Evaluate options

• First option: Matches the interpretation of vertical intercepts (starting balances).
• Second option: Slope is earnings per hour (10), not vertical intercept. Incorrect.
• Third option: No relation to vertical intercepts. Incorrect.

Answer:

Zoe started with $15 in her account and Chloe started with -$20 in her account.