Question

The graph below represents the number of balls thrown over time.
What is the slope?

What is the y-intercept?

Is it proportional?


1,5 2,10 3,15 4,20 5,25

Answer 1

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