Sec 3.7 Equations of Lines in the Coordinate Plane Chapter 3

Review Are parallel Two lines  to the same line are to each other. In a plane, two lines  to the same line are . If two lines are cut by a transversal they form special properties. Corresponding angles Alternate interior angles Alternate exterior angles Are congruent. Are parallel Same-side interior angles are supplementary.

Lesson Purpose Essential Question Objective How can you prove that two lines are parallel? Objective Write an equation of a line given characteristics of parallel or perpendicular lines.

What is a slope? The steepness of a hill

If you have ever walked up or down a hill, then you have already experienced a real life example of slope As you go up hill, you may feel like you are spending lots of energy to get yourself to move. The steeper the hill, the harder it is for you to keep yourself moving

Slope of Math Keeping this fact in mind, by definition, the slope is the measure of the steepness of a line. In real life, we see slope in any direction. However, in math, slope is defined from left to right. I repeat we always measure slopes going from left to right. This is very important! There are four types of slope you can encounter. A slope can be positive, negative, undefined or equal to zero. When the slope is equal to zero, we say that there is no slope

Different types of slopes A negative(-) slope: If you go from left to right  and you go down, it is a negative slope A positive(+) slope: If you go from left to right  and you go up, it is a positive slope

No Slope or Slope Undefined Vertical lines have no slope, or undefined slope. A zero (0) slope: If you go from left to right and you don't go up or down, it is a zero slope Ski Bird cannot ski vertically.  Sheer doom awaits Ski Bird at the bottom of a vertical hill.

Slope Equation A slope of a line contains two points (x₁, y₁) and (x₂ ,y₂).

Example #1 Step 1: use slope equation: Step 2: set up equation with points given: Step 3: solve What kind of slope is it? Let’s find the slope of the line passing through the given points. (2,3),(-1,-6)

Question #1 What is the slope of the line passing through the points (2, 7) and (21, 3)? A. 2/7 B. 3/4 C. 4/3 D. 1/3

Question #2 What is the slope of the line passing through the points (-2,-3) and (1, 3)? A. 1/2 B. 2 C. -2 D. -1/2

Example #2 What is the slope of the line?

Question #3 Find the slope of the line? A. 1/4 B. -1/4 C. -4 D. 4

Question #4 Find the slope of the line? A. 2/3 B. 3/2 C. -2/3 D. -3/2

3.8 Slopes of Parallel lines Parallel lines have the same slope.

Slopes of Perpendicular Lines The product of the slopes of two perpendicular lines is -1 or the slopes are negative reciprocal. Product means multiplication.

Slope-Intercept Form -is an equation of a non-vertical line is y=mx+b where m is the slope and b is y-intercept

Example #3 Graph the equation of the line y= ½x+2 Step 1: identify the slope and y-intercept Step 2 : plot your y- intercept Step 3: connect the points

Question #5 Graph the equation y= ½x-3 A. B C. D.

Question #6 Graph the equation y= -2x-2 B A D C

Real World Connections

Ticket Out and Homework pg. 207-208 #’s 5, 6, 7,9,10, 14, 15, 18,19,20,21 Is it always necessary to identify both the slope and y-intercept of a line when graphing its equation? Explain