Final answer:
The equation of the line that models Luke's bike ride is y = 6x - 1, representing a speed of 6 miles per hour with an initial starting point that suggests he may have started 1 mile before the origin point on the graph.
Step-by-step explanation:
To write the equation of the line that models Luke's bike ride, we need to find the slope and the y-intercept of the line. In this context, the 'slope' represents Luke's speed, and the 'y-intercept' represents his starting point on the highway, presuming the ride started from the origin.
First, we calculate the slope using the two points provided: (1, 5) after 1 hour and (3, 17) after 3 hours. The slope formula is (change in distance)/(change in time), which is (17 - 5)/(3 - 1) = 12/2 = 6. So, Luke's speed, or the slope of the line, is 6 miles per hour.
We can use the point-slope form of a line to determine the equation: y - y1 = m(x - x1). Using point (1, 5) and the slope m of 6, we get: y - 5 = 6(x - 1). We simplify this to get y = 6x - 1, which represents the equation of the line.
Therefore, the equation of the line that models Luke's bike ride is y = 6x - 1.