Question

the following table shows the number of feet a helicopter flies above the ground as a function of time:

time (in seconds) x	distance above ground (in feet) f(x)
2	16
4	14
6	12
8	10

find and interpret the meaning of the x - intercept in this scenario.
a (10, 0); the time it takes for the helicopter to reach the ground
b (18, 0); the time it takes the helicopter to take off
c (10, 0); the time it takes the helicopter to take off
d (18, 0); the time it takes for the helicopter to reach the ground
question 8 (1 point)
(02 04 mc)
choose the equation that represents the line passing through the point (2, - 5) with a slope of - 3.
a y=-3x - 13
b y=-3x + 11
c y=-3x + 13
d y=-3x + 1

Explanation:

Step1: Find the equation of the line for the helicopter - distance problem

We first find the slope $m$ using the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,18)$ and $(x_2,y_2)=(2,16)$. Then $m=\frac{16 - 18}{2-0}=\frac{-2}{2}=-1$. Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(0,18)$ (where $x_1 = 0$ and $y_1=18$), the equation of the line is $y-18=-1(x - 0)$, or $y=-x + 18$. To find the $x$ - intercept, we set $y = 0$. So, $0=-x + 18$, which gives $x = 18$. The $x$ - intercept represents the time when the helicopter reaches the ground.

Step2: Find the equation of the line for the second problem

The point - slope form of a line is $y - y_0=m(x - x_0)$, where $(x_0,y_0)=(2,-5)$ and $m=-3$. Substituting these values, we get $y-(-5)=-3(x - 2)$. Simplifying, $y + 5=-3x+6$, and then $y=-3x + 1$.

Answer:

1. d. $(18,0)$; the time it takes for the helicopter to reach the ground
2. d. $y=-3x + 1$