Assume that y is directly proportional to x. If and , determine a linear model that relates y and x.

Question

Assume that y is directly proportional to x. If  and  , determine a linear model that relates y and x.

Quizplus · Accepted Answer

If y is directly proportional to x, we can set up the equation y = kx, where k is a constant of proportionality.

We are given two pairs of values: (2, 6) and (5, 15). We can use either pair to solve for k.

Using (2, 6): 
6 = k(2) 
k = 3

Using (5, 15): 
15 = k(5) 
k = 3

Since we get the same value for k using either pair, we can be confident that k = 3.

Now that we know k, we can write the equation y = 3x. This equation represents a linear model that relates y and x, and the only answer choice that matches this equation is C: 11eb11e8_19ca_fbaa_ad38_bb5c7d06c749_TB4588_11.

Assume That Y Is Directly Proportional to X