Question

Dr. Shah visits patients at their homes. The equation y = 150x + 50 represents the
amount she charges, where y represents the total cost and x represents the number of
hours she spends at the home. When the equation is graphed, what does the y-intercept
represent?

the extra amount after the hourly rate

the rate for the entire visit

the rate for the first 20 minutes

the hourly rate only

Answer 1

In the equation \( y = 150x + 50 \), the variable \( y \) represents the total cost, \( x \) represents the number of hours Dr. Shah spends at the home, and the coefficients indicate the relationship between these variables.

The y-intercept of this equation occurs when \( x = 0 \). If we substitute \( x = 0 \) into the equation, we get:

\[
y = 150(0) + 50 = 50
\]

This means that when no hours are spent (0 hours), the total cost \( y \) is $50.

In the context of the situation, this y-intercept represents the fixed cost associated with the visit, which is likely a base fee that is charged regardless of the time spent at the patient's home.

Therefore, the y-intercept represents:

**the extra amount after the hourly rate.**

So the correct answer is: **the extra amount after the hourly rate.**