Transcript Document
Take Out Paper for Notes! Graphs and Linear Equations What do you remember about… On a number line, each point is the graph of a number. On a plane, each point is the graph of an ordered pair. Where would place the following?: x-axis Origin y-axis Quadrants Rene’ Descartes • French Mathematician and Philosopher • Use a coordinate system to combine algebra and geometry • Laid the foundation for analytic geometry Find 3 points that satisfy the following conditions: • The x-coordinate is the same as the y-coordinate • ( ) ( ) ( • The absolute values of the x-coordinate and the y coordinate are the same • ( ) ( ) ( • The product of the coordinates is 2 • ( ) ( ) ( ) ) ) Equations whose graphs are lines are called linear equations. • Linear • Non-Linear y 2x 1 y 3x 2 5 y 4 9 x 15 y 7 y 2x 1 2 x y 16 2 y 2 2 x xy 3 The solution of an equation with two variables is an ordered pair of numbers, which can be plotted on a coordinate plane. A graph of an equation is a drawing that represents its solutions. So…….. How many ways can we graph? Ways to graph… 1. T-table 2. Intercepts ( Using x and y intercepts) 3. Slope – Intercept ( Using the slope and y-intercept) 4. Point-Slope ( Using one point and the slope) T-table Example 1: y 3x 2 T-table • Example 2: 2 x 5 y 10 T-table • Example 3: y 1 2 x 1 Now it’s your turn…. HIT OR MISS…. Graphing by Intercepts • This method uses 2 very specific points on the graph. • x-intercept- point where the graph intersects the x-axis • y-intercept- point where the graph intersects the y-axis How do you find intercepts? • x-intercept… From the given equation, let y = 0 , then solve for x. 2 x 5 y 10 Let y 0 2 x 5(0) 10 2 x 10 x-intercept : (5,0) x5 How do you find intercepts? • y-intercept… From the given equation, let x = 0 , then solve for y. 2 x 5 y 10 Let x 0 2(0) 5 y 10 5 y 10 y-intercept : (0,-2) x 2 Example 4: 6 ,0 7 0, 3 7x 2y 6 Example 5: 1 3 3, 0 0, 4 x 1 4 y 1 Your turn …. MESSAGE IN CODE… GRAPH BY INTERCEPTS