Question

tyler is ordering a taxi from an online taxi service. he has to pay a flat charge just to order the taxi, and then has to pay per mile, depending on how far he travels, as is represented in the linear graph below. what is the meaning of the ( y )-value when ( x = 1 )?

Explanation:

Step1: Identify axes meaning

The x - axis is "Distance Traveled (miles)", so \(x = 1\) means 1 mile traveled. The y - axis is "Total Cost (\$)".

Step2: Interpret \(y\) at \(x = 1\)

The \(y\) - value at \(x=1\) represents the total cost Tyler has to pay when he travels 1 mile in the taxi. This includes the flat charge (the y - intercept, which is \$4.00 when LXI2) and the cost for 1 mile of travel. To find the slope (cost per mile), we can use two points. Let's take \((0,4)\) and \((5,20)\) (from the graph trend). The slope LXI3. So the equation is LXI4. When LXI5, \(y=3.2(1)+4=7.2\)? Wait, no, maybe my point selection is wrong. Wait, looking at the graph, when LXI6, LXI7 (flat charge). Let's find another point. Let's see, when LXI8, what's LXI9? The line goes to \((5,20)\)? Wait, no, the graph's y - axis at LXI10 is around \$20? Wait, maybe the slope is calculated as \(\frac{y_2 - y_1}{x_2 - x_1}\). Let's take \((0,4)\) and \((1,y)\). Wait, the key is the meaning, not the exact value. The \(y\) - value at \(x = 1\) is the total cost (flat charge + cost for 1 mile) when Tyler travels 1 mile. So the meaning is the total cost Tyler pays for traveling 1 mile in the taxi.

Answer:

The \(y\) - value when \(x = 1\) represents the total cost (in dollars) that Tyler has to pay for traveling 1 mile in the taxi (including the flat charge to order the taxi and the cost for 1 mile of travel).