A graph has time (hours) on the x-axis and total charge (dollars) on the y-axis. Points are at (0, 8), (2, 27), (4, 46), (6, 65).

Question

For the new year, the instructor is thinking of changing his rates. The equation of the possible new rates is represented in the graph. What is the y-intercept of the instructor's new rates as a ratio?

Answer 1

To determine the y-intercept of the instructor's new rates from the given points on the graph, we'll assume the relationship between time (hours) and total charge (dollars) can be represented by a linear equation in the form \( y = mx + b \), where \( b \) is the y-intercept.

The points provided are:

• (0, 8)
• (2, 27)
• (4, 46)
• (6, 65)

The y-intercept occurs when \( x = 0 \). From the provided point (0, 8), we can directly see that when the time is 0 hours, the total charge is 8 dollars. Therefore, the y-intercept \( b \) is 8.

As a ratio, the y-intercept can be expressed as:

\[ \frac{8}{1} \]

Hence, the y-intercept of the instructor's new rates as a ratio is \(\frac{8}{1}\).