1. 6.4
Standard Form

2. 6.4 – Standard Form
REVIEW: Slope-intercept form of a linear equation is
y = mx + b

3. 6.4 – Standard Form Standard Form of an equation: Ax + By = C
where A, B, & C are REAL #s and A & B are not 0. This is a good form to graph an equation QUICKLY.

4. Ax + By = C Standard Form Rules for Standard Form: No fractions
A is not negative (it can be zero, but it CANNOT be negative).
By the way, "integer" means no fractions, no decimals. Just clean whole numbers (or their negatives).

5. 6.4 – Standard Form
Using Standard Form, you can find the x-intercept and y-intercept, and then graph the equation.
To find the intercepts, you substitute 0 for both the x and y.

6. 6.4 – Standard Form Example: Find the x and y intercepts for
3x + 4y = 24.
To find the x intercept, substitute 0 for the y.
3x + 4(0) = 24
3x = 24
x = 8
So, when y = 0, x = 8. Your x-int. is (8, 0).

7. 6.4 – Standard Form To find the y-int. substitute 0 for the x
So your y-int is (0, 6)
Using your x and y-int, you can now graph the equation.

8. 6.4 – Standard Form

9. 6.4 – Standard Form
Example: Graph the equation
4x + 6y = 2

10. 6.4 – Standard Form
Using Standard Form, you can write equations for vertical and horizontal lines. (You can’t write vertical lines in slope-intercept form)

11. 6.4 – Standard Form Example: Graph the following y= -2 x = 4
When graphing these, say draw a line through the ___ - axis at the number.

12. 6.4 – Standard Form
If we are looking for the intercepts of an equation, standard from is the easiest to use. Therefore, we may want to change slope-intercept equations to standard form.

13. 6.4 – Standard Form Example: Write in Standard Form.
First we must move the x to the other side. So we add to both sides to get:

14. 6.4 – Standard Form
Now we must make the numbers whole. So we must multiply by 3 to get rid of the fraction.

15. Ex. 2: Write in standard form.
Given
4(y + 4) = 3(x – 2)
Multiply by 4 to get rid of the fraction.
4y + 16 = 3x – 6)
Distributive property
4y = 3x – 22
Subtract 16 from both sides
4y – 3x= – 22
Subtract 3x from both sides
– 3x + 4y = – 22
Format x before y
3x – 4y = 22
Multiply by -1 in order to get a positive coefficient for x.

16. Multiply by 3 to get rid of the fraction.
Ex. 3: Write the standard form of an equation of the line passing through (5, 4), -2/3
Given
3(y - 4) = -2(x – 5)
Multiply by 3 to get rid of the fraction.
3y – 12 = -2x +10
Distributive property
3y = -2x +22
Add 12 to both sides
3y + 2x= 22
Add 2x to both sides
2x + 3y = 22
Format x before y

17. Multiply by 2 to get rid of the fraction
Ex. 4: Write the standard form of an equation of the line passing through (-6, -3), -1/2
Given
2(y +3) = -1(x +6)
Multiply by 2 to get rid of the fraction
2y + 6 = -1x – 6
Distributive property
2y = -1x – 12
Subtract 6 from both sides
2y + 1x= -12
Subtract 1x from both sides
x + 2y = -12
Format x before y

18. Ex. 6: Write the standard form of an equation of the line passing through (5, 4), (6, 3)
First find slope of the line.
Substitute values and solve for m.
Put into point-slope form for conversion into Standard Form Ax + By = C
y – 4 = -1x + 5
Distributive property
y = -1x + 9
Add 4 to both sides.
y + x = 9
Add 1x to both sides
x + y = 9
Standard form requires x come before y.

19. Ex. 7: Write the standard form of an equation of the line passing through (-5, 1), (6, -2)
First find slope of the line.
Substitute values and solve for m.
Put into point-slope form for conversion into Standard Form Ax + By = C
11(y – 1) = -3(x + 5)
Multiply by 11 to get rid of fraction
11y – 11 = -3x – 15
Distributive property
11y = -3x – 4
Add 4 to both sides.
11y + 3x = -4
Add 1x to both sides
3x + 11y = -4
Standard form requires x come before y.

20. 6.4 – Standard Form Writing equations in the REAL WORLD:
You are working two jobs during the summer. You are mowing lawns and delivering newspapers. You make $12/hour mowing lawns and $5/hour delivering newspapers. If you made a total of $130, write an equation in standard form.
12x + 5y = 130

21. 6.4 – Standard Form Example #2:
You are training to participate in the annual Ironman Championship in Kona, Hawaii. You need to burn a total of 500 calories per day to get in proper shape. Write an equation in standard form to find the minutes you would need to workout each day if you were to just swim and run.

22. Calories burned per minute
6.4 – Standard Form
Activity
Calories burned per minute
Bicycling 10
Running 11
Hiking 7
Swimming 12
Walking 2
Rowing