1. 5.5 Standard Form:
X-intercept: The point where the graph crosses the x-axis, ( y=0).
Y-intercept: The point where the graph crosses the y-axis, (x=0).
Linear Equation: is an equation that models a linear function.

2. GOAL:

3. Ax + By = C Standard Form: The linear equation of the form:
Whenever we are given a graph we must be able to provide the equation of the function in
Standard Form: The linear equation of the form:
Ax + By = C
where A, B and C are real whole numbers (no fractions) and A and B are not both zero.

4. EX: What are the x- and y-intercepts of the graph of 5x – 6y = 60?

5. 5x – 6y = 60 plug in y=0 5x – 6(0) = 60 5x = 60 x = 60/5  12
SOLUTION: There are many ways to find this information depending on the form you are given, but if you are given the standard form (Ax+By=C), then you must plug in zero for the other variable.
Finding the x-intercept: plug in zero for y
5x – 6y = 60
plug in y=0
5x – 6(0) = 60
5x = 60
x = 60/5  12
(12,0) is the point.

6. 5x – 6y = 60 plug in x=0 5(0) – 6y = 60 – 6y = 60 y=60/-6  -10
Finding the y-intercept: plug in zero for x
5x – 6y = 60
plug in x=0
5(0) – 6y = 60
– 6y = 60
y=60/-6  -10
(0, -10) is the point

7. Graph:
𝟓𝒙−𝟔𝒚=𝟔𝟎
X-intercept: (12, 0) 2 -2 2
Y-intercept: ( 0, -10) -2

8. YOU TRY IT: What are the x- and y-intercepts of the graph of 3x + 4y = 24?

9. 3x + 4y = 24 plug in y=0 3x + 4(0) = 24 3x = 24 x = 24/3  8
YOU TRY IT: (SOLUTION)
Finding the x-intercept: plug in zero for y
3x + 4y = 24
plug in y=0
3x + 4(0) = 24
3x = 24
x = 24/3  8
(8,0) is the point.

10. 3x + 4y = 24 plug in X=0 3(0) + 4y = 24 4y = 24 y = 24/4  6
Finding the y-intercept: plug in zero for x
3x + 4y = 24
plug in X=0
3(0) + 4y = 24
4y = 24
y = 24/4  6
(0,6) is the point.

11. Graph:
3𝒙+𝟒𝒚=𝟐𝟒
X-intercept: (8, 0)
Y-intercept: ( 0, 6)

12. X = 3 y = - 2 Graphing Horizontal Lines
Remember: x lines are vertical y lines are Horizontal
X = 3
y = - 2

13. What are the graphs of x = -1 and y = 5
YOU TRY IT:
What are the graphs of x = -1 and y = 5

14. X = -1 y = 5 YOU TRY IT: (SOLUTION)
Remember: x lines are vertical y lines are Horizontal
X = -1
y = 5

15. TRANSFORMING TO STANDARD FORM
If we are given an equation in slope-intercept from (y = mx +b), and the point-slope form (y – y1=m(x-x1)) we can rewrite the equations into standard form:
Ax + By = C
where A, B and C are real whole numbers (no fractions) and A and B are not both zero.

16. EX: What are the standard forms of
1) y = - 𝟑 𝟕 x and 2) y – 2 = - 𝟏 𝟑 (x + 6)

17. SOLUTION: 1)
Using the slope-intercept from y = - 𝟑 𝟕 x + 5
We must get rid of any fraction, no fractions allowed:
y = - 𝟑 𝟕 x + 5
Inverse of dividing by 7
7y = - 3x + 35
Inverse subtraction 3x
7y + 3x= 35
Variables in order
Ax + By = C form.
3x + 7y = 35

18. 𝟑𝒙+𝟕𝒚=𝟑𝟓 X-intercept: (11.7, 0) Y-intercept: (0, 5) Here we would use:
Graph:
𝟑𝒙+𝟕𝒚=𝟑𝟓
X-intercept: (11.7, 0)
Y-intercept: (0, 5)
Here we would use:
y = - 𝟑 𝟕 x + 5 down 3, right 7

19. SOLUTION: 2) Using the point-slope from y-2 = - 𝟏 𝟑 (x + 6)
We must first distribute the slope
y -2 = - 𝟏 𝟑 x - 2
Distribute - 𝟏 𝟑
We must then get rid of fractions
Inverse of division by 3 (multiply everything by 3).
3y - 6 = - x -6
3y + X = -6 +6
Variables to left numbers to the right of equal sign.
x + 3y = 0
Ax + By = C form.

20. 𝒙+𝟑𝒚=𝟎 We now use y = - 𝟏 𝟑 x + 0 X-intercept: (0, 0)
Graph:
𝒙+𝟑𝒚=𝟎
X-intercept: (0, 0)
Y-intercept: (0, 0)
We now use y = - 𝟏 𝟑 x + 0

21. USING STANDARD FORM AS MODEL
In real-world situations we can write and use linear equations to obtain important information to help us find out what we can do with the resources we have.

22. EX:. In a video game, you earn 5 points for each jewel you find
EX: In a video game, you earn 5 points for each jewel you find. You earn 2 points for each star you find. Write and graph an equation that represents the number of jewels and stars you must find to earn 250 points.
What are three possible combinations of jewels and stars you can find that will earn you 250 points?

23. SOLUTION: In a video game, you earn 5 points for each jewel you find.
Let x = the jewels you find.
You earn 2 points for each star you find. Let y = the starts you find.
Write the equation for a total of 250 points:
5x + 2y = 250

24. 5𝒙+𝟐𝒚=𝟐𝟓𝟎 X-intercept: (50, 0) Y-intercept: (0, 125) Graph: Stars
250
225
200
175
150
125
100
Y-intercept: (0, 125) 75 50 25
Jewels 25 50 75
100
125

25. (25, 62.5) 25 Jewels, 62.5 Stars (25, 63) 25 Jewels, 62.5 Stars
Graph:
Three points are:
(0, 125) 0 Jewels, 125 Stars
Stars
250
225
200
(25, 62.5) 25 Jewels, Stars
175
150
125
100 75 50
(25, 63) 25 Jewels, Stars 25
Jewels 25 50 75
100
125

26. VIDEOS:
Graphs

27. CLASSWORK: Page
Problems: As many as needed to master the concept