Question

Can someone answer 15b

Answer 1

A)

well, we know the elevator's rate is -20 f/s, ok, so every second, is dropping 20 feet, therefore, "y" is "distance from the ground floor", so when y = 0, meaning the distance to the ground floor is 0, so you ARE at the ground floor then.

and "x" is how many seconds you've been in the elevator.

now, she got in the elevator for 6 seconds, so, the elevator went down by 20 * 6, or 120 feet down, reason why the slope is negative, when she stopped, she was 350 feet away from the ground floor still though.

if the elevator went down 120 feet, and she's still 350 feet from the ground floor, that means  she boarded the elevator at 120 + 350 feet, or 470 feet.

b)

$\bf \begin{array}{lcccllll} &\stackrel{\textit{elapsed seconds}}{x_1}&\stackrel{\textit{ft from ground-floor}}{y_1}\\ % (a,b) &({{ 6}}\quad ,&{{ 350}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -20 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-350=-20(x-6) \\\\\\ y-350=-20x+120\implies y=-20x+\stackrel{y-intercept}{470}$