Answer:
Explanation:
a. The equation of the line that describes the relationship between distance and time for Car X can be found by using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m), we can use the formula: m = (change in y) / (change in x) = (distance traveled) / (time elapsed) = 174 miles / 3 hours = 58 miles per hour.
Since the car starts at time x = 0 and has traveled 174 miles at time x = 3, the y-intercept (b) can be found by setting x = 0 and solving for y: y = 58x + b, and y = 174 when x = 3, so b = 174 - 58(3) = -160.
Putting it all together, we get the equation: y = 58x - 160.
b. The graph that represents the relationship between distance and time for Car X is a line that passes through the point (0, -160) and has a slope of 58. This line represents the linear relationship between the distance traveled and the time elapsed for Car X.
The y-intercept of -160 represents the distance traveled when time is equal to 0. The slope of 58 represents the rate of change of the distance traveled with respect to time. This means that for every hour that passes, Car X travels 58 miles.