1. 3.4 Graphing Linear Equations in Standard Form
Learning Goal: Students will be able to graph horizontal and vertical lines, graph linear equations in standard form using intercepts, and use linear equations to solve real life problems.

2. Standard Form Ax + By = C, where A, B and C are real numbers and where A and B are not both zero. What happens when x = 0 or y = 0? Horizontal Line (happens when x=0) The graph y = b is a horizontal line that passes through (0, b). Vertical Line (happens when y=0) The graph x = a is a vertical line that passes through (a, 0).

3. Example 1: Horizontal and Vertical Lines
a) Graph y = b) Graph x = -2
For every value of x, the y value is 4. This graph will be a horizontal line 4 units above the x-axis.
For every value of y, the x value is -2. This graph will be a vertical line 2 units to the left of the y-axis.
Hint: all values of x on this line will be the ordered pair (x, 4)
Hint: all values of y on this line will be the ordered pair (-2, y)

4. You try!
1) Graph y = ) Graph x = 5

5. Using Intercepts to Graph Equations
x-intercept
The x coordinate of a point where the graph crosses the x-axis. It occurs when y = 0.
y-intercept
The y coordinate of a point where the graph crosses the y-axis. It occurs when x = 0.
To graph the linear equation Ax + By = C, find the intercepts and draw a line that passes through them.
To find the x-intercept, let y = 0 and solve for x.
To find the y-intercept, let x = 0 and solve for y.

6. Example 2: Using Intercepts to Graph a Linear Equation
Use intercepts to graph
3x + 4y = 12
Step 1- Find the intercepts. x-intercept 3x + 4(0) = 12 3x = 12 x = 4 (4,0) y-intercept 3(0) + 4y = 12 4y = 12 y = 3 (0,3)
Step 2- Plot the points and draw the line.

7. Example 2: Using Intercepts to Graph a Linear Equation
b) Use intercepts to graph
2x – y = 4
Step 1- Find the intercepts. x-intercept 2x - 0 = 4 2x = 4 x = 2 (2,0) y-intercept 2(0) – y = 4 -y = 4 y = -4 (0,-4)
Step 2- Plot the points and draw the line.

8. You try!
3) Graph x + 3y = -9 using intercepts. x-intercept x + 3(0) = -9 x = -9 (-9, 0) y-intercept 0 + 3y = -9 3y = -9 y = -3 (0,-3)

9. Example 3: Solving Real Life Problems
You are planning an awards banquet for your school. You need to rent tables to seat 180 people. Tables come in two sizes. Small tables seat 6 and large tables seat 10 people. The equation 6x + 10y = 180, where x is the number of small tables needed and y is the number of large tables needed.
Graph the equation and interpret the intercepts.
x-intercepts
6x + 10(0) = 180
6x = 180
x = 30
(30, 0)
y-intercepts
6(0) + 10y = 180
10y = 180
y = 18
(0, 18)

10. Interpreting the x and y intercepts.
The x-intercept shows that you can rent 30 small tables when you do not rent any large tables.
The y-intercept shows that you can rent 18 large tables when you do not rent any small tables.

11. Example 3: Solving Real Life Problems
You are planning an awards banquet for your school. You need to rent tables to seat 180 people. Tables come in two sizes. Small tables seat 6 and large tables seat 10 people. The equation 6x + 10y = 180, where x is the number of small tables needed and y is the number of large tables needed. b) Find four possible solutions in the context of the problem.
Only whole-number values of x and y make sense in the context of the problem.
Besides the x and y intercepts, it looks like the line passes through (10, 12) and (20,6).
So, four possible combinations of tables that will seat 180 people are: 0 small and 18 large, 10 small and 12 large, 20 small and 6 large or 30 small and 0 large.

12. You try!
4) You decide to rent tables from a different company. The situation can be modeled by the equation 4x + 6y = 180, where x is the number of small tables and y is the number of large tables. Graph the equation and interpret the x and y intercepts. What are the 4 options for seating 180 people?
x-intercept
4x + 6(0) = 180
4x = 180
x = 45
(45 , 0)
y-intercept
4(0) + 6y = 180
6y = 180
y = 30
(0, 30)