Questiona. What does each of these points represent in this situation: $(0,0),(1,55)$ , and $(5,275)$ ? b. What is the constant of proportionality?
Mr. Brown's Road Trip c. What equation relates the distance, $y$ , and the time, $x$ ? $y=55 x$

Studdy Solution

STEP 1

1. The points $(0,0)$ , $(1,55)$ , and $(5,275)$ represent data points on a graph of Mr. Brown's road trip.
2. The relationship between distance $y$ and time $x$ is linear, as given by the equation $y = 55x$ .

STEP 2

1. Interpret what each point represents in the context of Mr. Brown's road trip.
2. Determine the constant of proportionality from the given equation.
3. Verify the equation relating distance and time.

STEP 3

The point $(0,0)$ represents the starting point of the trip, where no time has passed ( $x = 0$ ) and no distance has been traveled ( $y = 0$ ).
The point $(1,55)$ indicates that after 1 hour ( $x = 1$ ), Mr. Brown has traveled 55 miles ( $y = 55$ ).
The point $(5,275)$ shows that after 5 hours ( $x = 5$ ), Mr. Brown has traveled 275 miles ( $y = 275$ ).

STEP 4

The constant of proportionality is the rate at which distance increases with time. From the equation $y = 55x$ , the constant of proportionality is 55. This means Mr. Brown travels at a constant speed of 55 miles per hour.

STEP 5

The equation $y = 55x$ correctly relates the distance $y$ and the time $x$ , as it shows that for every hour of travel, the distance increases by 55 miles.
The constant of proportionality is:
$\boxed{55}$

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