Question

car x travels 174 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 mile(s). this means it will pass through the point. use the slope to move 3 units to the right of the origin and unit(s) up to find the point that can be used to graph the relationship.

Explanation:

Step1: Calculate the speed (slope)

The speed \(v=\frac{y}{x}\). Given \(y = 174\) miles and \(x=3\) hours, the speed \(v=\frac{174}{3}=58\) miles per hour.
The equation of a line in slope - intercept form is \(y = mx + b\). Since when \(x = 0\) (initial time), \(y=0\) (initial distance), \(b = 0\). So the equation is \(y = 58x\).

Step2: Analyze the graph

If a car travels for \(0\) hours, it will travel \(0\) mile(s). This means it will pass through the point \((0,0)\).
The slope \(m = 58=\frac{58}{1}\). Using the slope to move \(1\) unit to the right of the origin and \(58\) units up. But if we consider the ratio \(\frac{174}{3}\), when we move \(3\) units to the right of the origin (\(x = 3\)), we move \(174\) units up (\(y=174\)).
The first graph (with \(y\) - axis as distance and \(x\) - axis as time) is the correct one because the relationship is \(y\) (distance) as a function of \(x\) (time). The second graph has the axes labeled incorrectly ( \(y\) - axis should be distance and \(x\) - axis should be time for the relationship \(y = 58x\))

Answer:

a. The equation of the line is \(y = 58x\).
b. The first graph (with \(y\) - axis labeled "Distance (mi)" and \(x\) - axis labeled "Time (hr)") is the correct graph. If a car travels for \(0\) hours, it will travel \(0\) mile(s). This means it will pass through the point \((0,0)\). Use the slope to move \(3\) units to the right of the origin and \(174\) unit(s) up to find the point \((3,174)\) that can be used to graph the relationship.