Question

PLEASE HELP!!!! Luke is training for a long-distance bike race. On Tuesday, after riding for 1 hour, he has travelled 5 miles along a straight highway. After 3 hours, he has travelled 17 miles. Write the equation of the line that models Luke’s bike ride. What does the x represent? What does the y represent?

Answer 1

The equation of the line that models Luke's bike ride is y = 6x - 1, where x represents the time in hours, and y represents the distance in miles traveled.

Step-by-step explanation:

The question involves plotting Luke's bike ride distances over time and finding the equation of the line that models his journey. The two points we have are: (1 hour, 5 miles) and (3 hours, 17 miles). To determine the equation of a line, we use the slope-intercept form, which is y = mx + b, where m is the slope (rate of change of distance with respect to time) and b is the y-intercept (distance covered at the time which equals zero).

First, calculate the slope using the two given points:

• Slope (m) = (change in y) / (change in x) = (17 miles - 5 miles) / (3 hours - 1 hour) = 12 miles / 2 hours = 6 miles/hour.

Next, we use one point to find the y-intercept, b:

• 5 = 6(1) + b,
• b = 5 - 6,
• b = -1 mile.

Thus the equation of the line is y = 6x - 1.

In this context, x represents the time in hours and y represents the distance in miles traveled along the highway.

Answer 2

Answer: y=6x-1

Step-by-step explanation:

y=6x-1

x represents the time luke has been riding(hours) and the y represents the distance he has travelled (miles)