2.2 Find Slope and Rate of Change

2.2 Find Slope and Rate of Change

Example 1The roof of an entryway to an office building

has a rise of 40 feet and a run of 100 feet. What is its slope?

2.2 Find Slope and Rate of Change

Example 2What is the slope of the line passing through

the points (-4, -5), (6, -2)?

If (x1, y1) = (2, 1) and (x2, y2) = (-1, 3), would the slope be different?

2.2 Find Slope and Rate of Change

2.2 Find Slope and Rate of Change

2.2 Find Slope and Rate of Change

Example 3Without graphing , tell whether the line

through the given points rises, falls, is horizontal or is vertical. (1, 6), (8, -1) (-4, -3), (7, 1) (-5, 3), (-5, 1) (9, 2), (-9, 2)

2.2 Find Slope and Rate of Change

2.2 Find Slope and Rate of Change

Two lines that do not intersect are called parallel lines.

Two lines that intersect to form a right angle are called perpendicular lines.

Using slopes we can determine whether two different non vertical lines are parallel or perpendicular.

2.2 Find Slope and Rate of Change

2.2 Find Slope and Rate of Change

Example 4Tell whether the lines are parallel,

perpendicular or neither. Line 1: (-2, 1) and (0, -5); Line 2: (0, 1) and (-3, 10)

Line 1: (-5, 3) and (-2, -3); Line 2: (4, 11) and (-4, -5)

2.2 Find Slope and Rate of Change

If two lines are parallel what do we know about their y-intercepts?

If one of two perpendicular lines has a slope of 1/a and a<0, is the slope of the other line positive or negative?

2.2 Find Slope and Rate of Change

2.2 Find Slope and Rate of Change

Another term for slope is rate of change, where a rate is a ratio of two quantities that have different units.

Real life rate of change has units like miles per hour or degrees per pay.

2.2 Find Slope and Rate of Change

Example 5Predict the percent of forestland in New

Hampshire in 2005. 1983 – 87% forested 2001 – 81.1% forested.

2.2 Find Slope and Rate of Change

How do you determine whether two nonvertical lines are parallel or perpendicular?