To determine the value of the comic book when Lucy bought it, we need to find the y-intercept of the linear function represented by the given points on the graph.
The points provided are:
- (1, 40)
- (2, 55)
- (3, 70)
- (4, 85)
We can first find the slope (m) of the line using the points (1, 40) and (2, 55):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{55 - 40}{2 - 1} = \frac{15}{1} = 15 \]
Now we can use the slope and a point on the line to find the equation of the line in slope-intercept form \( y = mx + b \), where \( b \) is the y-intercept (the value when \( x = 0 \)).
Using the point (1, 40): \[ 40 = 15(1) + b \] \[ 40 = 15 + b \] \[ b = 40 - 15 = 25 \]
Thus, the equation of the line is: \[ y = 15x + 25 \]
To find the value of the comic book when Lucy bought it (which corresponds to \( x = 0 \)): \[ y = 15(0) + 25 = 25 \]
Therefore, the value of the comic book when Lucy bought it was $25.
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