Question

The table represents the total miles traveled, y, after a number of hours, x.

Hours, x
Miles, y
2.5
150
4.0
240
5.5
330
7.0
420

Which linear equation represents the situation?

y = 60 x
y = 60 x + 480
y = 4 x + 240
y = 270 x

Answer 1

To find the correct linear equation that represents the relationship between the total miles traveled \(y\) and the number of hours \(x\), we can analyze the data provided in the table.

The data points from the table are:

- (2.5, 150)
- (4.0, 240)
- (5.5, 330)
- (7.0, 420)

Let's first find the slope (rate of miles per hour) between two points. We'll take the points (2.5, 150) and (4.0, 240):

1. Calculate the change in miles:
\[ \Delta y = 240 - 150 = 90 \]
2. Calculate the change in hours:
\[ \Delta x = 4.0 - 2.5 = 1.5 \]

3. Now, we calculate the slope (m):
\[ m = \frac{\Delta y}{\Delta x} = \frac{90}{1.5} = 60 \]

This means for each hour, 60 miles are traveled. Thus, the equation can be written in the form:
\[ y = 60x + b \]

Next, we will find \(b\) (the y-intercept) using one of the points. Let's use the point (2.5, 150):
\[ 150 = 60(2.5) + b \]
\[ 150 = 150 + b \]
\[ b = 150 - 150 = 0 \]

Thus, the equation simplifies to:
\[ y = 60x \]

Given the answer choices, the correct equation that represents the situation is:
**y = 60x**.