Question

car x travels 144 miles in 3 hours.
a. write the equation of the line that describes the relationship between distance and time. use x for the time in hours and y for the distance in miles.
b. what is the graph that represents the relationship between distance and time for car x? explain

if a car travels for 0 hours, it will travel (0,0) mile(s). this means it will pass through the point \\(\square\\). use the slope to move 3 units to the right of the origin and \\(\square\\) unit(s) up to find the point \\(\square\\) that can be used to graph the relationship.

Explanation:

Part a:

Step1: Find the slope (speed)

The speed of Car X is distance divided by time. So, speed $m = \frac{144}{3} = 48$ miles per hour.

Step2: Write the linear equation

The general form of a linear equation is $y = mx + b$. Since at time $x = 0$ (0 hours), the distance $y = 0$ (because if a car travels for 0 hours, it goes 0 miles), so $b = 0$. Thus, the equation is $y = 48x$.

• When $x = 0$ (time = 0 hours), $y = 0$ (distance = 0 miles), so the line passes through the point $(0, 0)$.
• The slope (speed) is 48 miles per hour. If we move 3 units to the right (increase time by 3 hours), the distance increases by $m\times3 = 48\times3 = 144$ miles. So we move 144 units up from the origin $(0,0)$ to the point $(3, 144)$.
• The graph should be a straight line passing through the origin $(0,0)$ with a slope of 48. Among the given graphs, we need to check which one has the correct slope and passes through the origin. The second graph (with x - axis up to 4 and starting at (0,0)) is more consistent as the first graph has a non - zero y - intercept (starts above (0,0)) which is incorrect for this relationship (since at 0 time, distance is 0).
• For the fill - in - the - blanks: If a car travels for 0 hours, it will travel $\boldsymbol{0}$ mile(s). This means it will pass through the point $\boldsymbol{(0, 0)}$. Use the slope to move 3 units to the right of the origin and $\boldsymbol{144}$ unit(s) up to find the point $\boldsymbol{(3, 144)}$ that can be used to graph the relationship.

Answer:

The equation is $y = 48x$.

Part b: