Video Transcript
Anthony rides his bike at a steady rate of 15 miles per hour. The function 𝑦 equals 15𝑥 shows how time 𝑥 relates to the distance 𝑦. Which graph represents this function?
And then we have five graphs labeled (A) to (E). Let’s go back to the original function. We’re told it’s 𝑦 equals 15𝑥. We’re also told this function represents Anthony riding his bike at a steady rate of 15 miles per hour. For every one hour Anthony travels, this relates to the distance 𝑦.
So there are a couple of ways we can answer this question. One is to form a table of values. This table of values will link an input, here 𝑥, with an output value for 𝑦. Let’s look at what happens during the first three hours of the motion. We’ll choose zero, one, two, and three for our table of values. Beginning with 𝑥 equals zero, since the equation is 𝑦 equals 15𝑥, we can substitute 𝑥 equals zero in to get 𝑦 equals 15 times zero, which is zero. Similarly, choosing 𝑥 equals one, and we see that the output will be 𝑦 equals 15 times one, which is simply 15. Then, when 𝑥 is two, 𝑦 is 15 times two, which is 30. And when 𝑥 is three, 𝑦 is 15 times three, which is 45.
Now, let’s inspect these values for a moment. When 𝑥 increases by one, the value of 𝑦 increases by 15. This makes a lot of sense because the coefficient of 𝑥 is 15. In other words, the slope or the gradient of this graph is going to be 15.
Now that we have a table of values and we’ve clarified that these values are likely to be correct, let’s identify the coordinates through which our line must pass. They are zero, zero; one, 15; two, 30; and three, 45. And we now notice that graphs (A) and (E) have 𝑥-values that correspond to the 𝑦-values in our table. So we’re going to disregard those straightaway.
Plotting the coordinates we have on the remaining graphs (B) through (D), and we see that the correct graph must be graph (D). We also observe that the slope of this graph is indeed 15. For every one unit right, we must move 15 units up on the graph itself. So the function 𝑦 equals 15𝑥 is represented by graph (D).
