Analyzing Linear Equations Slope

What You'll Learn Slope Find the slope of a line. Use rate of change to solve problems.

If the pilot doesn’t change something, he / she will not make it home for Christmas. Would you agree? Consider the options: 1) Keep the same slope of his / her path. Not a good choice! 2) Go straight up. Not possible! This is an airplane, not a helicopter. There has got to be some “measurable” way to get this aircraft to clear such obstacles. Discuss how you might radio a pilot and tell him or her how to adjust the slope of their flight path in order to clear the mountain.

Fortunately, there is a way to measure a proper “slope” to clear the obstacle. We measure the “change in height” required and divide that by the “horizontal change” required.

Slope The steepness of a line is called the _____. slope Slope is defined as the ratio of the ____, or vertical change, to the ___, or horizontal change, as you move from one point on the line to another. rise run

Slope The slope m of the non-vertical line passing through the points and is

Slope

Slope Find the slope of the line that passes through (1, 1) and (3, 6). run = 3 - 1 = 2 units rise = 6 - 1 = 5 units Let (x1, y1) = (3, 6) and (x2 , y2) = (1, 1). This slope is said to be ________. positive

Slope Find the slope of the line that passes through (5, 2) and (2, 6). run = 2 - 5 = - 3 units rise = 6 - 2 = 4 units Let (x1, y1) = (5, 2) and (x2 , y2) = (2, 6). This slope is said to be ________. negative

Slope Find the slope of the line that passes through (1, 4) and (6, 4). run = 6 - 1 = 5 units rise = 4 - 4 = 0 units Let (x1, y1) = (1, 4) and (x2 , y2) = (6, 4). A horizontal line is said to have a slope of _____. zero

Slope Find the slope of the line that passes through (4, 2) and (4, 8). run = 4 - 4 = 0 units rise = 8 - 2 = 6 units Let (x1, y1) = (4, 2) and (x2 , y2) = (4, 8). The slope of a vertical line is said to be __________. undefined Notice: m = undefined. Division by zero is not possible.

Slope Find the value of r so that the line through (r, 7) and (4, 1) has a slope of – 3. run = 2 - 4 = -2 units rise = 7 - 1 = 6 units Let (x1, y1) = (4, 1) and (x2 , y2) = (r, 7). Substitute all known information Find the cross products Solve for r. Slope formula

Slope Slope can be use to describe a rate of change The rate of change tells, on average, how a quantity is changing __________. over time

Slope The graph shows the amount spent on food and drink at U.S. restaurants in recent years. Find the rate of change for 1980 – 1990. Spending on food and drink increased by $119 billion in a 10-year period for a rate of change of ____________________. $11.9 billion per year

End of Lesson Slope