1. Chapter-4(part 1) Graphing Linear Equations and Functions By: Donna, Fannie, Ashley and Nick

2. Coordinate Plane 4.1 Coordinate Plane 4.1 Key concept: page 207 Example 2 Key concept: page 207 Example 2 Plot Points in a Coordinate Plane. Describe the location of the point. Plot Points in a Coordinate Plane. Describe the location of the point. a. A(-4,4) b. B(3,-2) c. C(0,-4)

3. Coordinate Plane 4.1 Coordinate Plane 4.1 Solution Solution Begin at the origin. First move 4 units to the left, then 4 units up. Point A is in Quadrant II. Begin at the origin. First move 4 units to the left, then 4 units up. Point A is in Quadrant II. Begin at the origin. First move 3 units to the right, then 2 units down. Point B is in Quadrant IV. Begin at the origin. First move 3 units to the right, then 2 units down. Point B is in Quadrant IV. Begin at the origin. And move 4 units down. Point C is on the y-axis. Begin at the origin. And move 4 units down. Point C is on the y-axis.

4. Coordinate Plane 4.1 Key concept: Page 208 example 4 Key concept: Page 208 example 4 Graph a function represented by a table Graph a function represented by a table Years before or since 1920 -12 -8 -4 0 4 8 12 Votes (millions) 15 15 19 27 29 37 40 Years before or since 1920 -12 -8 -4 0 4 8 12 Votes (millions) 15 15 19 27 29 37 40  Explain how you know that the table represents a function.  Graph the function represented by the table.  Describe any trend in the number of votes cast. Solution a. The table represents a function because each input has exactly one output. b. To graph the function, let X be the number of years before or since 1920. Let Y be the number of votes cast (in millions). c. In the 3 election yrs before 1920, the no. of votes cast was less than 20 million. In 1920, the no. of votes cast was greater than 20 million. The no. of votes cast continued to increase in the 3 election yrs since 1920.

5. Graphing Linear Equations using tables 4.2 Key concept: Page 216 Example 3 Key concept: Page 216 Example 3 Graph y=b and x=a Graph (a) y=2 and (b) x=-1. Solution  For every value of x, the value of y is 2. The graph of the equation y=2 is a horizontal line 2 units above the x-axis.

6. Graphing Linear Equations using tables 4.2 Key vocabulary: Vertical & Horizontal Lines Key vocabulary: Vertical & Horizontal Lines Equations of Horizontal and Vertical Lines Equations of Horizontal and Vertical Lines The graph of y = b is a horizontal line. The line passes through the point (0,b) 1)A y – int. of a graph is the y-coordinate of a point where the graph crosses the y-axis. 1)A y – int. of a graph is the y-coordinate of a point where the graph crosses the y-axis. The graph of x = a is a vertical line. The line passes through the point (a, 0). 2) An x – int. of a graph is the x-coordinate of a point where the graph crosses the x-axis. 2) An x – int. of a graph is the x-coordinate of a point where the graph crosses the x-axis.

7. Graphing using intercepts 4.3 Key concept: Page 225 Example 1 Find the intercepts of the graph of an equation solution a. To find the x-intercept, substitute 0 for y and solve for x. b. To find the y-intercept, substitute 0 for x and solve for y.

8. 4.3 Key concept : Page 226 Example 2 Use intercepts to graph an equation (graph the equation x+2y = 4) solution 1 st find the intercepts. x+2y=4 x+2(0)=4 0+2y=4 x=4 y=2 2 nd plot points. The x -int. is 4, so plot the point (4,0). The y -int. is 2, so plot the point (0,2). Draw a line through the points.