Question

The graph shows a proportional relationship between the number of miles Marco bikes and the number of hours. What equation relates the distance, y, and the time, x?

Answer 1

The equation showing the proportional relationship between the distance Marco bikes (y) and the number of hours (x) is y = mx, where m is the constant speed at which he bikes.

Step-by-step explanation:

The student is asking for an equation that represents a proportional relationship between the distance Marco bikes, denoted as y, and the number of hours, denoted as x. Since the graph shows a straight line, we can use the equation y = mx + b, where m is the slope and b is the y-intercept. In this case, the y-intercept is zero because the graph starts at the origin, indicating that Marco hasn't traveled any distance at time zero. The slope of the graph, m, represents the rate at which Marco bikes, which is the constant speed. Therefore, the equation is y = mx, or if we want to use specific units, like in the equation y = (2.0 km/min) x, we would write it y = (2.0 km/min) × t where t represents time.

Answer 2

The equation relating the distance (y) and time (x) is (y = kx). K is the constant of proportionality.

In a proportional relationship between distance (y)and time (x), the equation takes the form (y = kx).

Where; (k) is the constant of proportionality.

Therefore, the equation relating the distance (y) and time (x) is (y = kx).

Where (k) represents the constant of proportionality determined by the situation or graph.