3. You are going to plant trees in your hilly backyard. Tree A is located at coordinates (1,4) and Tree B is located at (5,12). What is the slope of the hill between the two trees?
slope = (12-4)/(5-1) = .....
To find the slope of the hill between Tree A and Tree B, we need to calculate the change in height (vertical distance) divided by the change in distance (horizontal distance) between the two trees.
Step 1: Calculate the change in height (vertical distance):
The vertical distance is the difference in the y-coordinates of the two trees.
Vertical distance = y-coordinate of Tree B - y-coordinate of Tree A
= 12 - 4
= 8
Step 2: Calculate the change in distance (horizontal distance):
The horizontal distance is the difference in the x-coordinates of the two trees.
Horizontal distance = x-coordinate of Tree B - x-coordinate of Tree A
= 5 - 1
= 4
Step 3: Calculate the slope:
Slope = Change in height / Change in distance
= Vertical distance / Horizontal distance
= 8 / 4
= 2
Therefore, the slope of the hill between Tree A and Tree B is 2.