Any questions on the Section 3 2 homework Section 3 1 Homework Issues Graphing non linear equations Graphs of absolute value equations Graphs of quadratic equations Compare to y x 4 Compare to y x3 4 Now please CLOSE YOUR LAPTOPS and turn off and put away your cell phones Sample Problems Page Link Dr Bruce Johnston Section 3 3 Graphing Linear Equations A linear function is a function that can be written in the form f x mx b Example Graph the following functions on the same pair of axes f x 2x g x 2x 3 h x 2x 5 y x Where do each of these graphs intersect the y axis At 0 0 0 3 and 0 5 respectively These are referred to as the y intercepts When a linear function is written in the form of f x mx b or y mx b the y intercept is 0 b How would we find the y intercept if the line is not written in the form f x mx b or y mx b Since all points on the y axis have an x coordinate of 0 substitute x 0 into the linear equation and find the corresponding y coordinate Example Find the y intercept of 4 x 3y Let x 0 Then 4 x 3y becomes 4 0 3y replace x with 0 4 3y simplify the right side 4 divide both sides by 3 3 y 4 So the y intercept is 0 3 Correspondingly all points on the x axis would have a y coordinate of 0 So to find an x intercept of a linear function we would substitute y 0 into the equation and find the corresponding x coordinate Example Find the x intercept of 4 x 3y Let y 0 Then 4 x 3y becomes 4 x 3 0 replace y with 0 4 x simplify the right side So the x intercept is 4 0 Example Graph the linear equation 4 x 3y by plotting intercepts We previously found that the y intercept is 0 the x intercept is 4 0 4 3 and Plot both of these points and then draw the line through the 2 points Note You should still find a 3rd solution to check your computations Example cont Graph the linear equation 4 x 3y Along with the intercepts for the third solution let y 1 You can use any value for x or y that you want to find a third point so pick something that will make your calculation easy Then 4 x 3y becomes 4 x 3 1 4 x 3 4 3 x 7 x replace y with 1 simplify the right side add 3 to both sides simplify the left side So the third solution is 7 1 4 3 Now we plot the two intercepts 0 and 4 0 along with the third solution 7 1 y 4 0 4 3 0 And then we draw the line that contains the three points 7 1 x Example Graph 2x y by plotting intercepts To find the y intercept let x 0 2 0 y 0 y so the y intercept is 0 0 To find the x intercept let y 0 2x 0 x 0 so the x intercept is 0 0 Oops It s the same point What do we do Example cont Since we need at least 2 points to graph a line we will have to find at least one more point Let x 3 Again you can pick any value for x that you want 2 3 y 6 y so another point is 3 6 Let y 4 2x 4 x 2 so another point is 2 4 Now we plot all three of the solutions 0 0 3 6 and 2 4 y And then we draw the line that contains the three points 3 6 2 4 0 0 x Example Graph y 3 Note that this line can be written as y 0 x 3 The y intercept is 0 3 but there is no x intercept Since an x intercept would be found by letting y 0 and 0 can t equal 0 x 3 there is no x intercept Every value we substitute for x gives a y coordinate of 3 The graph will be a horizontal line through the point 0 3 on the y axis Example cont y 0 3 x Example Graph x 3 This equation can be written x 0 y 3 When y 0 x 3 so the x intercept is 3 0 but there is no y intercept Any value we substitute for y gives an x coordinate of 3 So the graph will be a vertical line through the point 3 0 on the x axis Example cont y 3 0 x Example from today s homework Vertical lines Appear in the form of x c where c is a real number x intercept is at c 0 no y intercept unless c 0 y axis Horizontal lines Appear in the form of y c where c is a real number y intercept is at 0 c no x intercept unless c 0 x axis Using the online graphing tool When the problem asks you to graph x and y intercepts you MUST graph these two points For example in this problem you would have to graph 0 1 and 4 0 If you used 0 1 and 4 2 you d get the same line but the computer would mark your answer wrong Solving for y gives y 1 5 x 3 5 Choose x 2 to get y 2 5 3 5 5 5 1 Choose x 7 to get y 7 5 3 5 10 5 2 Or choose x 3 to get y 3 5 3 5 0 5 0 Note The homework for this section shouldn t take too long so you might want to look ahead at section 3 4 on slopes of lines and section 3 5 on slope intercept equations of lines Reminder This homework assignment on Section 3 3 is due at the start of next class period This assignment is entirely online with no worksheet However you should do the work for each problem in your notebook and keep these notes to study for quizzes and tests You may now OPEN your LAPTOPS and begin working on the homework assignment