Slope of a Line The slope of a nonvertical line is a measure of the number of units the line rises or falls vertically for each unit of horizontal change from left to right. Let’s look at a diagram. y (x2, y2) y2 y2 – y1 (x1, y1) y1 x2 – x1 I remember this stuff. x x1 x2 The slope m of a nonvertical line passing through the points (x1, y1) and (x2, y2) is

Types of Slope That was easy There are four different types of slope. Let’s take a look at a sample of each type. 4 3 2 1 -1 (0, 4) 4 3 2 1 -1 (3, 1) (-2, 0) -2 -1 1 2 3 4 -2 -1 1 2 3 4 (1, -1) The slope is positive because the line rises from left to right. The slope is negative because the line falls from left to right. 4 3 2 1 -1 4 3 2 1 -1 That was easy (3, 3) (-1, 2) (2, 2) (3, 1) -2 -1 1 2 3 4 -2 -1 1 2 3 4 The slope is zero because the line is horizontal. The slope is undefined because the line is vertical.

Equations of Lines y-intercept Slope-Intercept Form of the line Used when the slope and the y-intercept are known. slope of the line known x coordinate Point-Slope Form slope of the line Used when the slope and the coordinates of one point in the form (x, y) are known. known y coordinate

Finding an Equation of a Line Find an equation of the line that has a slope of 3 and passes through the point (1, -2). Since the slope and the coordinates of one point are known, you can start out with the Point-Slope Form. Replace m, x1, and y1 with the given information. Simplify the resulting equation. Solve the resulting equation for y. Your final result is in Slope-Intercept Form.

Ratios and Rates of Change What’s the difference? The slope of a line can be interpreted as either a ratio or a rate of change. If the x-axis and the y-axis have the same unit of measure, the slope has no units and therefore is a ratio. If the x-axis and the y-axis have different units of measure, the slope is a rate or a rate of change. I’m still a little confused, but let’s continue anyway.

Rate of Change Example That was easy The population of Arizona was 1,775,000 in 1970 and 2,718,000 in 1980. Over this 10-year period, what was the average rate of change? Let’s look at a diagram. 4 3 2 1 That was easy Population (in millions) 1970 1980 1990 Rate of Change = 94,300 people per year Year

Ratio Example In tournament water-ski jumping, the ramp rises to a height of 6 feet on a raft that is 21 feet long. Find the slope of the ski ramp. 6 ft 21 ft Since the x-axis and the y-axis have the same unit of measure, the slope has no units and therefore is a ratio.

Homework Page 16: 1 – 6, 9 – 14, & 19 Do Not Plot Points for 9 - 14

Graphing Linear Models Use the slope-intercept form of an equation to sketch a graph. Example 3 Example 1 Example b That was easy

Summary of Equations of Lines General Form Vertical Line Horizontal Line Point-Slope Form Slope-Intercept Form

Parallel and Perpendicular Lines Two distinct nonvertical lines are parallel if and only if their slopes are equal. Two distinct nonvertical lines are perpendicular if and only if their slopes are negative reciprocals. The lines are parallel The lines are perpendicular

Parallel & Perpendicular Lines Examples Write the general forms of the equations of the lines through the point (a) parallel to the given line and (b) perpendicular to the given line. Parallel Perpendicular Point Line Asi de Facil

Homework Page 17: 36 -44 & 62 -64 Even Numbers Only Do Not Sketch the Graph

Writing Equations of Lines Write the equation of the line that goes through the given point and has the given slope. Write the equation in: (a) Point Slope Form (b) Slope-Intercept Form (c) General Form That was easy

More Writing Equations of Lines Write the equation of the line that goes through the given points. Write the equation in: (a) Point Slope Form (b) Slope-Intercept Form (c) General Form There’s 2 different points. Which one do I use? You can use either one. Asi de Facil Holy Schnikies! It’s the same answer.

Even More Writing Equations of Lines Write the equation of the line that goes through the given points. Write the equation in: (a) Point Slope Form (b) Slope-Intercept Form (c) General Form Now let’s try the other point. That was easy Holy Schnikies! It’s the same answer again.