2.4: Linear Equation Graphs Linear Equation: Graph forms a Line EXAMPLES: y = 2x + 1, y = -x, 3x - 4y = 10 Nonlinear Equation: Graph does NOT form a line EXAMPLES: y = x2; xy = 3; y = 4/x; y2 = x

Graphing Using Intercepts Maybe you’ve noticed that all of our graphs touch the x and y axes. We can use this to make graphing easier! x-intercept: Where the graph touches the x-axis To find the x-intercept: Plug in y = 0 & solve EXAMPLE: Find the x-intercept of 4x + 3y = 12 SOLUTION: 4x + 3(0) = 12. 4x = 12 x = 3; x-intercept is: (3, 0) The x-intercept is always (#, 0)

Using Intercepts to Graph y-intercept: Where the graph touches the y-axis To find the y-intercept: Plug in x = 0 and solve EXAMPLE: Find the y-intercept of 4x + 3y = 12 SOLUTION: 4(0) + 3y = 12. 3y = 12 y = 4; y-intercept is: (0, 4) The y-intercept is always (0, #)

Using Intercepts To Graph We can use the information we just found to graph the equation. EXAMPLE: Graph 4x + 3y = 12 using intercepts SOLUTION: x-intercept was (3, 0); y-intercept was (0, 4)

Graphing Using Intercepts YOUR TURN: I. Find the x and y intercepts. II. Graph the equation using the intercepts. 1. 2y = 3x - 6 2. 5x + 7y = 35 3. 8x + 2y = 24 SOLUTIONS: 1. x-intercept: (2, 0); y-intercept: (0, -3) 2. x-intercept: (7, 0); y-intercept: (0, 5) 3. x-intercept: (3, 0); y-intercept: (0, 12)

Graphing Using Intercepts 1. 2y = 3x - 6 2. 5x + 7y = 35 3. 8x + 2y = 24

Horizontal Lines: y = number You may have noticed that all of our lines have been slanted. So how do we get sideways (horizontal) lines? Horizontal Lines: y = number EXAMPLE: 1. Graph y = 3 2. Graph y = -2

Vertical Lines: x = number OK, so how do we get up and down (vertical) lines? Vertical Lines: x = number EXAMPLE: 1. Graph x = 1 2. Graph x = -3

Horizontal and Vertical Lines YOUR TURN: Please graph each equation and state whether it is horizontal or vertical. 1. y = 4 2. x = -2 3. x = 0 4. y = -1 5. y = 0 6. x = 5