Question

The cost of riding in a cab is $3.00 plus $0.75 per mile. The equation that represents this relation is y = 0.75x +3, where x is the number of miles traveled and y is the cost of the trip. Look at the graph of the equation and determine whether the relation is a function.

Answer 1

Answer:

Yes, the relation is a function.

Step-by-step explanation:

Given:

The equation that represents the cost of riding a cab is given as:

$y=0.75x+3$

Where, 'x' is the number of miles traveled and 'y' is the the total cost of the trip.

The above equation represents a line as it is of the form $y=mx+b$ which represents a line with constant slope.

Now, in order to plot this equation, we need at least two points.

Now, let $x =0$, then

$y=0.75(0)+3=3$. So, (0, 3) is a point on the line.

Let $x =1$, then

$y=0.75(1)+3=3.75$. So, (1, 3.75) is a point on the line.

Plot these two points on a graph and draw a line passing through these two points.

Now, for a relation to be a function, it should pass the vertical line test.

According to vertical line test, vertical lines passing through the graph must cut the graph at only 1 point for the graph to represent a function.

Here, we observe that vertical lines passing through the line will intersect the line only at one point. So, it represent a function.