1. Lesson 1-3
Formulas

2. Introduction to Formulas
You will need to memorize three formulas.
Distance formula, Midpoint formula, Slope formula

3. Coordinate Plane
All three formulas use ordered pairs on the coordinate plane.

4. Distance Formula Example: Find the distance between (-3, 2) and (4, 1)
The formula: d =
Example: Find the distance between (-3, 2) and (4, 1)
Answer: x1 = -3, x2 = 4,
y1 = 2 and y2 = 1
D =
D =
D =

5. Midpoint Formula The formula: M = Example: Find the midpoint
between (-2, 5) and (6, 4)
Answer: x1 = -2, x2 = 6,
y1 = 5, and y2 = 4
M =
M =

6. Slope Formula The formula: m = Example: Find the slope between
(-2, -1) and (4, 5)
Answer: m =
m =

7. Describing Lines
Lines that have a positive slope rise from left to right.
Lines that have a negative slope fall from left to right.

8. Describing Lines
Lines that have no slope (the slope is undefined) are vertical.
Lines that have a slope equal to zero are horizontal.

9. Some More Examples
Find the slope between (4, -5) and (3, -5) and describe it.
m =
Since the slope is zero,
the line must be horizontal.

10. Example 2
Find the slope between (3,4) and (3,-2) and describe the line.
m =
Since the slope is undefined,
the line must be vertical.

11. Example 3
Find the slope between (1,5) and (6,3) and describe the line.
m =
Since the slope is negative,
the line is falling from left to right.

12. Try These Problems Find the distance between (3, 2) and (-1, 6)
Find the midpoint between (7, -2) and (-4, 8)
Find the slope between (-3, -1) and (5, 8) and describe the line.
Find the slope between (4, 7) and (-4, 5) and describe the line.
Find the slope between (6, 5) and (-3, 5) and describe the line.