Question

start by finding the change in vertical and horizontal distance from (1, 3) to (3, 9). In other words, what is the change in number of pieces of candy and the total cost from (1, 3) to (3, 9)?
x
y
m
(1, 3)(3, 9)
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
Number of pieces of candy
Total cost
Slope
=
vertical distance
horizontal distance

Answer 1

To find the change in vertical and horizontal distances from the point (1, 3) to the point (3, 9), we will compute the changes in the x-coordinates and y-coordinates, which represent the number of pieces of candy and total cost, respectively.

1. **Horizontal Distance (change in x)**:
- The x-coordinates are 1 and 3.
- Change in x = \(3 - 1 = 2\).

2. **Vertical Distance (change in y)**:
- The y-coordinates are 3 and 9.
- Change in y = \(9 - 3 = 6\).

Now that we have the changes, we can set the values:

- Horizontal Distance: 2 (this represents the change in the number of pieces of candy)
- Vertical Distance: 6 (this represents the change in total cost)

Next, we can calculate the slope (m) using the formula for slope:

\[
m = \frac{\text{vertical distance}}{\text{horizontal distance}} = \frac{6}{2} = 3
\]

Therefore, summarizing the results:

- Change in Number of Pieces of Candy: 2
- Change in Total Cost: 6
- Slope (m): 3