Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. 3-5 Lines in the Coordinate Plane 4. Practice 5. EXIT

Practice

3-5 Lines in the Coordinate Plane Chapter 3 3-5 Lines in the Coordinate Plane

Slope The steepness of a line

Types of Slope Positive Negative Zero No

Equations of Lines A line is a set of points. Every line has an equation that relates the coordinates of these points. ex: x + y = 5 (1, 4) (4, 1) (3, 2) (2, 3) (0, 5) (5, 0)

Forms of a Line These are each different forms of the same equation. x + y = 5 Standard form y = -x + 5 Slope-Intercept form y – 3 = -1(x -2) Point-Slope form

Standard Form This equation is of the form Ax + By = C. The x and y terms are on the left side and the constant is on the right side of the equation. x + y = 5

Slope-Intercept Form This equation is of the form y = mx + b. The y term is on the left and the x term is on the right side of the equation. The value of m is the slope of the equation. The value of b is the y-intercept. y = -x + 5

Point-Slope Form This equation is of the form y – y1 = m(x – x1). The y term is on the left and the x term is on the right side of the equation. The value of m is the slope of the equation. The values x1 and y1 are the coordinates of a point on the line. y – 3 = -1(x – 2) m = -1 (2, 3)

Example #1 Graph.

Example #2 Graph.

Example #3 Graph.

Example #4 Graph.

Example #5 Graph.

Example #6 Graph.

Example #7 Find the equation of a line with slope -8 that contains the point (3, -6).

Example #8 Find the equation of a line that contains the points (4, -9) and (-1, 1).

Example #9 Find the equation of a line with slope -1 that contains the point (2, -4).

Example #10 Find the equation of a line that contains the points (5, 0) and (7, -3).

Example #11 Find the equation of a horizontal line through the point (5, -1).

Example #12 Find the equation of a vertical line through the point (-7, -5).

Example #13 A wheelchair ramp is being constructed at a local hospital. What is the equation of the line that represents the ramp?

Example #14 The equation C = $0.50d + $0.75 represents the cost (C) for purchasing d number of donuts at the local bakery. What is the slope of the line represented by this equation? What does the slope represent in this situation? What is the y-intercept of the line? What does the y-intercept represent in this situation?

Practice WB 3-5 # 1, 2, 9, 11, 19, 25, 26, 33 EXIT