rachel is a stunt driver. one time, during a gig where she escaped from a building about to explode(!), she…

rachel is a stunt driver. one time, during a gig where she escaped from a building about to explode(!), she drove to get to the safe zone at 24 meters per second. after 4 seconds of driving, she was 70 meters away from the safe zone. let y represent the distance (in meters) from the safe zone after x seconds. complete the equation for the relationship between the distance and number of seconds.

rachel is a stunt driver. one time, during a gig where she escaped from a building about to explode(!), she drove to get to the safe zone at 24 meters per second. after 4 seconds of driving, she was 70 meters away from the safe zone. let y represent the distance (in meters) from the safe zone after x seconds. complete the equation for the relationship between the distance and number of seconds.

Answer

Explanation:

Step1: Find the speed

The speed is calculated by the change in distance over time. She drove 70 - 24 = 46 meters in 4 seconds. So the speed $v=\frac{70 - 24}{4}=\frac{46}{4}=11.5$ meters per second.

Step2: Form the linear - equation

The general form of a linear equation for distance $y$ in terms of time $x$ is $y = mx + b$, where $m$ is the speed and $b$ is the initial distance from the safe - zone. Here, $m=- 11.5$ (negative because the distance to the safe zone is decreasing) and when $x = 4$, $y = 70$. We can find $b$ by substituting into the equation: $70=-11.5\times4 + b$. Solving for $b$ gives $b=70 + 11.5\times4=70 + 46 = 116$. So the equation is $y=-11.5x + 116$.

Answer:

$y=-11.5x + 116$