Question

philip is a tech geek and loves his new smartphone, but he is frustrated by how slowly the battery charges. after coming home from school, philip notices that the battery level is low, so he plugs in his phone to charge the battery. this graph shows the relationship between the total time (in hours) that philip charges his phone, x, and the battery level (as a percent of its full capacity), y. do x and y have a proportional relationship?

Explanation:

Step1: Recall proportional relationship

A proportional relationship between \(x\) and \(y\) means \(y = kx\) (where \(k\) is constant), and the graph should pass through the origin \((0,0)\).

Step2: Check the graph's y - intercept

From the graph, when \(x = 0\) (no charging time), the battery level \(y=6\) (not \(0\)). Also, the graph is a curve (not a straight line through the origin), so the relationship between \(x\) and \(y\) does not satisfy \(y = kx\) for a constant \(k\).

Answer:

No, \(x\) and \(y\) do not have a proportional relationship.