To analyze the graph you provided with the points (x, y) representing the number of balls thrown over time, we can look at the coordinates:
- (1, 5)
- (2, 10)
- (3, 15)
- (4, 20)
- (5, 25)
Finding the Slope
The slope (m) of a line is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the first two points (1, 5) and (2, 10):
\[ m = \frac{10 - 5}{2 - 1} = \frac{5}{1} = 5 \]
Finding the Y-Intercept
The y-intercept is the value of y when x = 0. Since the given points are linear and it appears they originate from the origin (0,0), we can deduce that:
- The y-intercept is 0.
Is it Proportional?
A relationship is proportional if it can be expressed in the form \(y = kx\), where k is a constant (the slope), and it passes through the origin (0,0).
Since the line formed by the given points does pass through the origin (0,0) and it maintains a constant ratio between y and x (the slope is constant), we can conclude that:
- Yes, the relationship is proportional.
Summary
- Slope: 5
- Y-Intercept: 0
- Is it Proportional? Yes
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