1. Lines, Lines, Lines!!! ~ Standard Form
Another equation of the
same line.

2. What we Have Learned so far….
Slope Intercept Form
Where m is the slope and b is the intercept

3. What we Have Learned so far….
Point-Slope Form
Where m is the slope and are a point on the line.

4. We will use our prior knowledge of
Slope-Intercept Form
&
Point-Slope Form
To learn about the Standard Form of a Line:
Ax + By = C

5. Standard Form The Standard Form of a Linear Equation is Ax + By = C
Where A ≥ 0,
&
A and B are not both zero
A, B, and C are integers whose greater common factor is 1.

6. Standard Form Notice that: x and y have exponents of 1
The Standard Form of a Linear Equation is
Ax + By = C
Notice that:
x and y have exponents of 1
x and y are not multiplied together
x and y do not appear in denominators, exponents, or radicals

7. Examples of Standard Form
These Equations are not in Standard Form:
1/2x + 2/3y = 6
12x – 36y = 10
5ix + 7py = -29
These Equations are in Standard Form:
2x + 5y = 7
x – y = - 10
1000x + 75y = 6

8. Question:
Is the equation 4x + 7y = -10 a linear equation? Explain why.
This equation is a linear equation because it is in standard form with A = 4, B = 7, and C = –10.
Is the equation 2xy = 4 a linear equation? Explain why.
This equation is not a linear equation because x and y are multiplied by each other.

9. Writing an equation in Standard Form Ax + By = C
y = 2/5x - 3
(5)y = (2/5x - 3)5
5y = 2x - 15
5y -2x = 2x -2x – 1
-2x + 5y = -15
-1(-2x + 5y = -15)
2x – 5y = 15
A= 2, B= -5, and C = 15

10. Writing an equation in Standard Form Ax + By = C Given A Point and a Slope
Point (3,4) and m = 6
y - y1 = m(x - x1)  Use Point-Slope Form
y - 4 = 6(x - 3)  Substitute the values
y - 4 = 6x – 18  Use Distributive Property
y = 6x  Add Liked Terms
y = 6x – 14  Slope-Intercept Form
-6x + y = 6x – 6x – 14  Move the x value
-6x + y = -14  Add Liked Terms
-1(-6x + y = -14)  Multiply times -1
6x – y = 14  Standard Form

11. Writing an equation in Standard Form Ax + By = C Given Two Points (6, -2) and (-4, 4)
First: Find the Slope between the two points
Second: Use the Slope and the first point on the Point-Slope Form. Plug them in.

12. Writing an equation in Standard Form Ax + By = C Given Two Points (6, -2) and (-4, 4)
 A = 3, B = 5 and C = 28

13. • • Steps to Graph Equations in standard form
Write the equation in standard form
Find x-intercept, by letting y = 0, solve for x, plot the point where x crosses the x-axis
Find y-intercept, by letting x = 0, solve for y, plot the point where y crosses the y-axis
Draw a line through the 2 points.
Graph 2 x + 3 y = 12
Already using standard form: 2 x + 3y = 12
Let y = 0 2 x + 3(0) = 12
2 x = 12
x = 6
x-intercept is at ( 6 , 0 )
Let x = 0 2 (0) + 3 y = 12
3 y = 12
y = 4
y-intercept is at ( 0 , 4 ) •
( 0 , 4 )
2 x + 3 y = 12 •
( 6 , 0 ) 13

14. Your Turn! How do you graph a line which is in standard form?
Graph 3x - 4y = -12
x y 3
(3)0 - 4y = -12 -4
3x - (4)0 = -12
Graph the points and connect the dots

15. Student Activity
You will now receive a worksheet. Turn the worksheet in when completed.

16. Do Not Disturb Work In Progress