To find the equation relating the number of hours Gwen worked (h) to the total number of tickets she sold (t), we can observe the values from the chart.
Looking at the data:
- When h = 1, t = 23
- When h = 2, t = 46
- When h = 3, t = 69
- When h = 4, t = 92
We can see that for each additional hour worked, the number of tickets sold increases by 23. This indicates a linear relationship.
To express this relationship as an equation, we can use the slope-intercept form of a linear equation, which is:
\[ t = mh + b \]
where:
- \( m \) is the slope (the rate of change),
- \( b \) is the y-intercept (the value of t when h = 0).
From the data, we see that Gwen sells 23 tickets for every hour she works. Therefore, the slope \( m = 23 \).
To find the y-intercept \( b \), we can assume that if Gwen did not work any hours, she would not sell any tickets. Thus, when \( h = 0 \), \( t = 0 \), which gives us \( b = 0 \).
Now, we can write the equation:
\[ t = 23h \]
This equation represents the relationship between the number of hours Gwen worked (h) and the total number of tickets she sold (t).
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