Suppose you have an after school baby sitting service. You charge a flat fee of $10 per week plus $3 per hour. The equation y = 3x + 10 represents your earnings per week for one child.

The $10 dollar charge is the Y-intercept (0,10). Meaning that would be the starting point on your graph in $. Then for every hour worked its an extra 3 dollars, so rise over run 3 over 1. Which would mean every hour worked (x-axis) would juust increase by three.

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You're on the right track with your assumption that the y intercept represents the situation where no hours were worked (x=0). In this case, the y intercept is the point (0, 10).

To describe the y intercept, we need to understand what the point (0, 10) represents in the context of the problem. In this scenario, the $10 charge is the flat fee per week, regardless of the number of hours worked. Therefore, when no hours are worked (x=0), the y-value (earnings per week) is $10.

So, when x (hours worked) is zero, the y intercept (earnings per week) is $10. It represents the baseline earning of $10 even if no hours are contributed.