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Math 142–Rodriguez Lehmann–1.2 Graphing Linear Equations A. Solutions to equations a. Ordered pairs are written as (x,y) where x is the independent variable and y is the dependent variable. b. An ordered pair (a,b) is a ____________ of an equation if the values a and b make the equation a true statement. (2,3) is a solution to x+y=5 c. We say that (2,3) _______________ the equation. d. The _______________ _____ of an equation is the set of all solutions to the equation. e. Solutions can be plotted on a coordinate system. Example: Find solutions to x + y = 5. Plot them. B. Graph a linear equation a. The graph of an equation in two variables is a visual way to represent _____ the _______________ of the equation. b. If an equation can be put into the form y=mx+b, where m and b are constants (numbers), then the graph of the equation is a __________. Graph the equation by hand. Verify your graph using ZStandard followed by ZSquare on a graphing calculator. Example 1: 1 y=− x+2 3 c. Example 2: 2( y − 3 ) = 4( x + 1 ) Example 3: −x + 2 y = 6 What about equations that look like x= # and y = #? Example: Find points that satisfy x=2. Plot them. The graph of x = # is a ____________________ line. The graph of y = # is a _____________________ line. Lehmann – 1.2 Page 2 of 4 Example 4: Graph y=–2. Example 5: Find an equation of the line sketched. y y x x d. Recap: If the equation can be put into the form y=mx+b or x=a, where m, b, and a are constants (numbers), then its graph is a line. These are called ____________ equations in two variables. e. Recap: The graph is a visual to represent the solutions to the equation. Which points represent ordered pairs that satisfy the equation? C. Find and interpret intercepts a. The x-intercept is the point where the graph intersects the x-axis. ( , ) To find it: let ___________ and solve for ___. b. The y-intercept is the point where the graph intersects the y-axis. ( , ) To find it: let ___________ and solve for ___. y x Lehmann – 1.2 Page 3 of 4 Find all x-intercepts and y-intercepts. Example 1: 4x – 6y = –12 Example 2: Example 3: y = 3x – 6 Example 4: x = 2 y=–3 c. When graphing equations we can find the intercepts instead of finding random points. d. Interpreting Intercepts Example 6: A person lowers their hot-air balloon by gradually releasing air from it. Let x be the number of minutes that he has been releasing the air from the balloon, and let y be the altitude of the balloon (in feet). Assume the relationship between x and y is described by the equation y=–150x+750. a. Graph the equation by hand. b. Find the y-intercept. What does it mean in this situation? c. Find the x-intercept. What does it mean in this situation? Lehmann – 1.2 Page 4 of 4