1. 6-4: Standard Form
Essential Question: How do we convert from y-intercept to standard form?

2. 6-4: Standard Form
Slope-Intercept form is just one form of a linear equation. Another form is standard form, which is useful in making quick graphs.
Standard Form
Ax + By = C, where A, B and C are integers
You use the x- and y-intercepts to make a graph. The x-intercept is the x-coordinate where the line crosses the x-axis.
You can also find the x-intercept by setting y = 0 and solving

3. 6-4: Standard Form Example 1: Finding x- and y-intercepts
Find the x- and y-intercepts of 3x + 4y = 8
x-intercept (set y=0 and solve)
3x + 4(0) = 8
3x = 8
x = 8/3
y-intercept (set x=0 and solve)
3(0) + 4y = 8
4y = 8
y = 2

4. 6-4: Standard Form Your Turn
Find the x- and y-intercepts of 4x – 9y = -12
x-intercept
x=-3
y-intercept
y=4/3

5. 6-4: Standard Form
If the x- and y-intercepts are integers, you can use them to make a quick graph
Example 2: Graphing Lines Using Intercepts
Graph 2x + 3y = 12
Step 1: Find the intercepts Step 2: Plot the intercepts
x-intercept
2x + 3(0) = 12
2x = 12
x = 6
y-intercept
2(0) + 3y = 12
3y = 12
y=4

6. 6-4: Standard Form
Your Turn
Graph 5x + 2y = -10

7. 6-4: Standard Form Example 3: Graphing Horizontal and Vertical Lines
y = x = 2
No x-intercept, so the No y-intercept, so the graph doesn’t cross the graph doesn’t cross the x-axis y-axis

8. 6-4: Standard Form
You can change equations in slope-intercept form into standard form.
If the equations contains fractions or decimals, multiply by the denominator(s) to only use integers
Then, add/subtract the x term so that both x and y are on the same side of the equation
Example 4: Transforming to Standard Form
Write y = ¾ x + 2 in standard form
Multiply each term by 4 (the denominator)
4y = 3x + 8
Subtract 3x from each side
-3x + 4y = 8

9. 6-4: Standard Form Your Turn Write y = -2/5 x + 1 in standard form
2x + 5y = 5

10. 6-4: Standard Form
Assignment
Worksheet #6-4
1 – 31, odd problems