Question

arnav starts with 5 dollars in his account. he earns 10 dollars per hour mowing lawns and deposits the earnings into his account. sarah starts with -15 dollars in her account. she earns 10 dollars per hour mowing lawns and deposits the earnings into her account. what are the vertical intercepts of the lines? arnav: $d = 5 + 10x$ the slope of arnav’s line is 10. the vertical intercept of arnav’s line is \boxed{}. sarah: $d = -15 + 10x$ the slope of sarah’s line is 10. the vertical intercept of sarah’s line is \boxed{}.

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the vertical intercept (the value of $y$ when $x = 0$).

Step2: Find the vertical intercept of Arnav's line

Arnav's equation is $d=5 + 10x$. Comparing with $y=mx + b$, when $x = 0$, we substitute $x = 0$ into the equation: $d=5+10\times0=5$. So the vertical intercept of Arnav's line is 5.

Step3: Find the vertical intercept of Sarah's line

Sarah's equation is $d=- 15+10x$. Comparing with $y = mx + b$, when $x = 0$, we substitute $x = 0$ into the equation: $d=-15 + 10\times0=-15$. So the vertical intercept of Sarah's line is - 15.

Answer:

The vertical intercept of Arnav’s line is 5.
The vertical intercept of Sarah’s line is - 15.