To determine the slope of the graph that represents Jeremy's total earnings based on the number of games he worked, we need to find the rate of change of his earnings per game. The slope of a graph in this context is essentially the change in earnings divided by the change in the number of games.
We are provided with two data points:
1. Jeremy earns [tex]$140 by working 4 games.
2. Jeremy earns $[/tex]210 by working 6 games.
To find the slope [tex]\( m \)[/tex], we use the formula for the slope of a line, which is:
[tex]\[ m = \frac{{\text{change in earnings}}}{{\text{change in number of games}}} \][/tex]
Let's define the points based on the given data as [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
- [tex]\( (x_1, y_1) = (4, 140) \)[/tex]
- [tex]\( (x_2, y_2) = (6, 210) \)[/tex]
Now calculate the change in earnings and the change in the number of games:
[tex]\[ \text{change in earnings} = y_2 - y_1 = 210 - 140 = 70 \][/tex]
[tex]\[ \text{change in number of games} = x_2 - x_1 = 6 - 4 = 2 \][/tex]
Using these values, we can now calculate the slope [tex]\( m \)[/tex]:
[tex]\[ m = \frac{70}{2} = 35 \][/tex]
Thus, the slope of the graph representing Jeremy's total earnings based on the number of games worked is [tex]\( 35 \)[/tex].
Therefore, the correct answer is:
C. 35
