Slope of a Line. Slopes are commonly associated with mountains.

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Presentation transcript:

Slope of a Line

Slopes are commonly associated with mountains.

Definitions of Slope The tilt or inclination of a line The ratio of vertical change to horizontal change. The change in y over the change in x

Vertical Change Horizontal Change Vertical Change Horizontal Change This ratio is also known as Rise Run

Vertical Change or the Rise Horizontal Change or the Run 4 3 Vertical Rise Horizontal Run 3 4

Positive Negative Zero Undefined or No Slope Types of Slope

Formal Definition of Slope Given two points (x 1, y 1 ) and (x 2, y 2 ), the slope m of a line is defined to be:

Slope – Example Given two points A(-3, -4) and B(3, 5), find the slope of the line through the points. Algebraically: Reduce fractions whenever possible.

Parallel lines Lines in the same plane that do not intersect are called parallel lines. Parallel lines have the same slope.

Perpendicular Lines Lines that intersect at right angles are called perpendicular lines. The slopes of these lines are opposite reciprocals. Opposite reciprocals???? 3….. -1/3 4

From the given equations, determine if the corresponding lines are parallel, perpendicular, or neither. y = 2x + 2 y = 4x – 2 2x + 6y = 1 4x + 12y =3 neither perpendicular parallel

Equations of Lines

Review of Slope-Intercept Form Review of Slope-Intercept Form The slope-intercept form of a linear equation is y = mx + b. m represents the slope b represents the y-intercept

m = -4, b =3 m = -, b = 5 Rewrite as y = -8x, m = -8, b = Rewrite as y = x + 0, m =, b = 0 Rewrite as y = 0x + 5, m = 0, b = 5 Review of Slope-Intercept Form y = -4x + 3 y = 5 – x 8x + y = y = x y = 5 Name the slope and y-intercept of each equation :

Writing Equations – Example 1 Use the Point-Slope Formula: is the given point Substitute m and into the formula

Example 1 Write the equation of the line with slope = -2 and passing through the point (3, -5). Substitute m and into the Point-Slope Formula.

Calculate the slope of the two points. Use one of the points and the slope to substitute into the Point-Slope formula. Writing Equations – Example 2

Write the equation of the line that goes through the points (3, 2) and (5, 4). Writing Equations – Example 2

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