Lesson 1 3 Formulas Lesson 1 3 Formulas

Lesson 1 -3 Formulas Lesson 1 -3: Formulas 1

The Coordinate Plane Definition: In the coordinate plane, the horizontal number line (called the x- axis) and the vertical number line (called the y- axis) interest at their zero points called the Origin. y - axis Origin x - axis Lesson 1 -3: Formulas 2

The Distance Formula The distance d between any two points with coordinates and is given by the formula d = . Example: Find the distance between (-3, 2) and (4, 1) x 1 = -3, x 2 = 4, y 1 = 2 , y 2 = 1 d= d= d= Lesson 1 -3: Formulas 3

Midpoint Formula In the coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates and. Example: Find the midpoint between (-2, 5) and (6, 4) x 1 = -2, x 2 = 6, y 1 = 5, and y 2 = 4 M= M= Lesson 1 -3: Formulas 4 are

Slope Formula Definition: In a coordinate plane, the slope of a line is the ratio of its vertical rise over its horizontal run. Formula: The slope m of a line containing two points with coordinates the formula and is given by where . Example: Find the slope between (-2, -1) and (4, 5). Lesson 1 -3: Formulas 5

Describing Lines l Lines that have a positive slope rise from left to right. l Lines that have a negative slope fall from left to right. l Lines that have no slope (the slope is undefined) are vertical. l Lines that have a slope equal to zero are horizontal. Lesson 1 -3: Formulas 6

Some More Examples l Find the slope between (4, -5) and (3, -5) and describe it. m= Since the slope is zero, the line must be horizontal. l Find the slope between (3, 4) and (3, -2) and describe the line. m= Since the slope is undefined, the line must be vertical. Lesson 1 -3: Formulas 7

Example 3 : Find the slope of the line through the given points and describe the line. (7, 6) and (– 4, 6) Solution: m y up 0 (– 4, 6) left 11 (-11) (7, 6) x This line is horizontal. Lesson 1 -3: Formulas 8

Example 4: Find the slope of the line through the given points and describe the line. (– 3, – 2) and (– 3, 8) Solution: right 0 y (– 3, 8) m up 10 x (– 3, – 2) undefined This line is vertical. Lesson 1 -3: Formulas 9

Practice l Find the distance between (3, 2) and (-1, 6). l Find the midpoint between (7, -2) and (-4, 8). l Find the slope between (-3, -1) and (5, 8) and describe the line. l Find the slope between (4, 7) and (-4, 5) and describe the line. l Find the slope between (6, 5) and (-3, 5) and describe the line. Lesson 1 -3: Formulas 10