Question

while driving to soccer practice, stevens mom slows down as she approaches a red light. this situation can be modeled as a linear relationship. complete the statement that describes the situation. the car is traveling at ▲ miles per hour when stevens mom starts slowing down. as stevens mom slows down, the cars speed decreases by ▲ miles per hour every second.

Explanation:

Step1: Find the initial speed

From the graph, when \(x = 2\) (seconds), \(y=30\) (miles per hour).

Step2: Calculate the rate of change

The formula for the slope \(m=\frac{\Delta y}{\Delta x}\). Let's take two points \((x_1,y_1)=(2,30)\) and assume another point as the car stops. But for the rate of decrease (negative slope in terms of speed - time as speed is decreasing). The speed changes from \(y = 30\) at \(x = 2\). If we consider the general linear relation \(y=mx + b\). Since it's a linear relationship of the form \(y=v_0+at\) (where \(v\) is speed, \(t\) is time, \(a\) is acceleration). The slope of the line (considering speed as a function of time) gives the rate of change of speed.
The car's speed \(y\) and time \(x\) (in seconds). The slope \(m=\frac{30 - 0}{2-0}=15\) (but since speed is decreasing, the rate of decrease is \(15\) miles per hour per second.

Answer:

The car is traveling at \(30\) miles per hour when Steven's mom starts slowing down. As Steven's mom slows down, the car's speed decreases by \(15\) miles per hour every second.