1. Lesson 6-3 Standard Form of a Linear Equation

2. What is Standard Form? Ax + By = C
It’s when your x’s and y’s are on the same side equal to a number. Your x must be positive! x goes first!

3. Why do we have to know Standard Form?
Standard Form is REALLY easy to graph is you use x- and y-intercepts.
X-intercept is where the graph crosses the x-axis.
Y-intercept is where the graph crosses the y-axis.

4. What are the coordinates?
When something crosses the x-axis, what is the coordinate?
(x, 0) The y is always zero.
When something crosses the y-axis, what is the coordinate?
(0,y) The x is always zero.

5. How to graph using Standard Form:
Find the y-intercept.
Find the x-intercept.
Plug in zero for x.
Ex. 2x + 3y = -2
2(0) + 3y = -2
0 + 3y = -2
3y = -2
y = -2/3
Plug in zero for y.
Ex. 2x + 3y = -2
2x + 3(0) = -2
2x + 0 = -2
2x = -2
x = -1

6. You try…Graph 3x + 4y = 8 X-int…plug in 0 for y Y-int…plug in 0 for x
3x + 4(0) = 8 3x + 0 = 8 3x = 8 X = 8/3 or
3(0) + 4y = y = 8 4y = 8 Y = 2
Now graph it! 

7. You try…Graph -4x + 3y = 12 X-int. (y=0) Y-int. (x=0)
-4x = 12 Divide by -4 X = -3
3y = 12 Divide by 3 Y = 4
Now graph it! 

8. Weird Graphs y = 4 x = -2 Where does it cross the y-axis?
Where does it cross the x-axis?

9. Classwork/Homework
pg. 301
2-18 even, all

10. It’s easier than you think…
If you think this is confusing and you’re more comfortable with y=mx+b, then change standard to y=mx+b!
It’s easier than you think…

11. Convert Into Slope-Intercept Form
(divide both sides by 2 to get y alone)
(now simplify all fractions)

12. *** Check Your Answer ***
-3y = -9x - 12
(divide both sides by -3 to get y alone)
(now simplify all fractions)
-3y = -9x - 12
y = 3x + 4
Slope = 3
Intercept = 4

13. *** medium *** 21x – 7y =14 -7y = -21x + 14 y = 3x – 2
Convert to Slope-Intercept Form:
21x – 7y =14
(subtract both sides by 21x)
(now divide both sides by -7)
-7y = -21x + 14
(simplify all fractions)
y = 3x – 2

14. Now you should be able to:
Define standard form
Define x- and y-intercepts
Know how to solve the standard form of a linear equation for the x- and y-intercepts
Graph using x- and y-intercepts
Change standard form to y=mx+b form then graph the linear equation from there