Hiking from Point to Point
How do you go from one point to another?
OBJECTIVE: To learn the slope formula—the math behind 'rise over run'
NOW it's time to introduce the math behind the 'rise over run' concept.
Mathematically, 'rise over run' refers to the ratio of change in y to change in x. In symbols,
where m = slope and (x₁, y₁) and (x₂, y₂) are the coordinates of two points.
where m = slope and (x₁, y₁) and (x₂, y₂) are the coordinates of two points.INSTRUCTIONS:
1. Plot each pair of points (x,y) in the applet below.
2. Use the applet to obtain the 'rise' and the 'run' between each pair of points and then compute the slope. The first has been done for you.
3. List these data values on a worksheet patterned after the table below.
Pair (x₁, y₁) (x₂, y₂) rise run slope
A ( 7, 8) ( 1, 5) -3_ -6_ __1/2__
B ( 5, 3) (-2, 4) ___ ___ _______
C (-3, -5) (-1, 8) ___ ___ _______
D ( 0, -5) ( 7, 8) ___ ___ _______
E ( 2, 0) ( 2, -3) ___ ___ _______
F (-8, -1) (-6, 3) ___ ___ _______
G ( 2, 4) ( 2, -3) ___ ___ _______
H ( 7, -1) (-8, -1) ___ ___ _______
I ( 7, -4) ( 1, -4) ___ ___ _______
J ( 4, -3) (-2, -9) ___ ___ _______
NOTE: The signs of 'rise' and 'run' may be interchanged, but the slopes will remain the same.
QUESTION: Given two points, how do you calculate the 'rise' between them? Briefly explain.
QUESTION: Given two points, how do you calculate the 'run' between them? Briefly explain.
INSTRUCTIONS:
1. On a separate sheet of paper, determine the slope of the line that passes through the given points.
2. Enter this slope as a ratio in the text-box provided.
3. If you enter a correct ratio, a big "Correct!" sign will appear.
4. Click on the "New Problem" button to generate a new problem.
Repeat until you have mastered the concept.
2. Enter this slope as a ratio in the text-box provided.
3. If you enter a correct ratio, a big "Correct!" sign will appear.
4. Click on the "New Problem" button to generate a new problem.
Repeat until you have mastered the concept.TODAY you discovered the math behind the 'rise over run' concept.
In future lessons, you'll have more opportunities to master this concept. We hope you ENJOYED this lesson.