Question

Kent is riding his bicycle. The graph shows the relationship between time in hours and the miles Kent rides.  Write an inequality to show the number of hours when Kent has ridden more than 30 miles. Explain your answer. 



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Answer 1

The inequality to represent the number of hours when Kent has ridden more than 30 miles is y = 6x for x > 5, where x is the number of hours ridden and y is the distance in miles.

Step-by-step explanation:

Step 1:

First, we need to plot the coordinates of the line on the graph.

We plot the points that fall exactly on an x axis value and also on a y axis value.

There are three such points on the given graph; (5, 30), (10, 60) and (15, 90). These points fall exactly on the values of the x axis and the y axis.

Step 2:

Now, we establish a relationship between the values of x (the number of hours ridden) and y (distance in miles).

Here y is the dependent value and x is the independent value i.e. the value of y values according to the values of x.

In 5 hours, Kent rode 30 miles. In 10 hours, he rode 60 miles and in 15 hours he rode 90 miles.

Step 3;

So for every 5 hours, Kent rides another 30 miles.

So y = 6x for x>5 is the

When x = 10, y = 6 × 10 = 60 miles,

When x = 15, y = 6 × 15 = 90 miles.