1. 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

2. 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)

3. 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, #)

4. 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)

5. Graphing Using Intercepts
YOUR TURN:
I. Find the x and y intercepts.
II. Graph the equation using the intercepts.
1. 2y = 3x x + 7y = x + 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)

6. Graphing Using Intercepts
1. 2y = 3x x + 7y = x + 2y = 24

7. 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 = Graph y = -2

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

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