1. Warm-Up 4.1
1. 𝟎°
2. 𝟒𝟑𝟕℉
3. −𝟒𝟎℃

2. Section 4.1 The Coordinate Plane
Goal: Plot points in a coordinate plane.

3. Coordinate System (a.k.a. Cartesian Plane):
x–axis is the horizontal axis y–axis is the vertical axis
Intersection of x–axis and y–axis is the Origin.
Ordered Pair (x, y) defines points in the plane.
y–axis
Quadrant II
(–, +)
Quadrant I
(+, +)
x–axis
origin
(0, 0)
Quadrant III
(–, –)
Quadrant IV
(+, –)

4. Ordered Pair (x, y) defines points in the plane.
Graphing Points–
Ordered Pair (x, y) defines points in the plane.
right (+) or
left (–)
up (+) or
down (–)
A (4, 5) 1st Quadrant
B (–2, –3) 3rd Quadrant
C ( –4, 6) 2nd Quadrant
D (0, –3) y–axis
E (1, –6) 4th Quadrant
F (5, 0) x–axis C A F D B E

5. Equations with Two Variables–
x is called the independent or control variable
y is called the dependent variable.

6. Scatter Plot- a graph used to determine a relationship between two sets of data.x 1 4 5 7 8 10 y 2 11 15 19 x 1 4 7 -4 -1 3 y 8 -2 10 13 x 1 4 5 -2 -8 y 8 2 10 2 2 2 2 2 2
Positive Correlation-
as x increases, y increases
Negative Correlation-
as x increases, y decreases
No Correlation-
no linear pattern

7. Time for some Guided Practice!!!
The Coordinate Plane
Time for some
Guided Practice!!!

9. Warm-Up 4.2
𝒚=−𝟐𝒙+𝟏𝟎
𝒚=𝟐𝒙+𝟏
𝒚=−𝟏𝟎
𝒚=𝟏𝟔

10. Graphing Linear Equations
Section 4.2
Graphing Linear Equations
Goal: Graph a linear equation using a table of values.

11. A linear equation in x and y is an equation that can be written in the
Graphing Linear Equations
A linear equation in x and y is an equation that can be written in the
form of 𝐴𝑥+𝐵𝑦=𝐶, where A and B are not both zero.
A solution of an equation in two variables is an ordered pair (x, y)
that makes the equation true.

12. Graphing Linear Equations

13. Graphing Equations with Two Variables–
1) Solve the equation for y. (called function form)
2) Make a table of points.
3) Connect the points from left to right with a line.
y = 3x – 4 x
y = 3x – 4 y
(2, 2)
0 y = 3(0) – 4 –4 (0, –4)
1 y = 3(1) – 4 –1 (1, –1)
2 y = 3(2) – 4 2 (2, 2)
–1 y = 3(–1) – 4 –7 (–1, –7)
(1, –1)
(0, –4)
(–1, –7)

14. x y 0 –2 (0, –2) 2 –1 (2, –1) 4 0 (4, 0) (4, 0) –2 –3 (–2, –3) (0, –2)
0 –2 (0, –2)
2 –1 (2, –1)
4 0 (4, 0)
–2 –3 (–2, –3)
(4, 0)
(0, –2)
(2, –1)
(–2, –3)

15. Time for some Guided Practice!!!
Graphing Linear Equations
Time for some
Guided Practice!!!

16. Warm-Up 4.3
𝟔,𝟎 , 𝟔,𝟏 ,(𝟔,𝟐)
−𝟏,𝟎 , −𝟏,𝟏 ,(−𝟏,𝟐)
𝟎,−𝟕 , 𝟏,−𝟕 ,(𝟐,−𝟕)
𝟎,𝟏𝟎 , 𝟏,𝟏𝟎 ,(𝟐,𝟏𝟎)

17. Graphing Horizontal and
Graphing Horizontal & Vertical Lines
Section 4.3
Graphing Horizontal and
Vertical Lines
Goal: Graph horizontal and vertical lines.

18. Vertical Lines: Written in the form of x = h.
Horizontal Lines: Written in the form of y = k. (constant function)
y = 2 x
0x + y = 2 y
0 0(0) + y = 2 2 (0, 2)
1 0(1) + y = 2 2 (1, 2)
5 0(5) + y = 2 2 (5, 2)
–3 0(–3) + y = 2 2 (–3, 2)
(0, 2)
(5, 2)
(–3, 2)
(1, 2)

19. x = 6 x
x = 6 y
6 x = 6 0 (6, 0)
6 x = 6 1 (6, 1)
6 x = 6 5 (6, 5)
6 x = 6 -3 (6, –3)
(6, 5)
(6, 1)
(6, 0)
(6, –3)

20. Horizontal
Vertical
y = 2 y = – y = 8
x = 6 x = –4 x = . 5

21. Time for some Guided Practice!!!
Graphing Horizontal & Vertical Lines
Time for some
Guided Practice!!!

22. Warm-Up 4.4 8 4

23. Graphing Lines Using Intercepts
Section 4.4
Graphing Lines Using Intercepts
Goal: Find the intercepts of the graphs of linear equations.

24. x–intercept– Where the graph intersects the x–axis.
Let y = 0 to get the point (x, 0)
y–intercept– Where the graph intersects the y–axis.
Let x = 0 to get the point (0, y)

25. Graphing Lines Using Intercepts

26. Graphing Lines Using Intercepts

27. How to Graph a Line with Intercept Method:
1. Find the x–intercept & y–intercept.
2. Draw the line.
3x – 2y = 12
Let y = 0.
3x – 2(0) = 12
3x = 12
x = 4
(4, 0)
Let x = 0.
3(0) – 2y = 12
–2y = 12
y = –6
(0, –6)

28. 4x + 3y = 24
Let y = 0.
4x + 3(0) = 24
4x = 24
x = 6
(6, 0)
Let x = 0.
4(0) + 3y = 24
3y = 24
y = 8
(0, 8)

29. 6y – x = 9
Let y = 0.
6(0) – x = 9
–x = 9
x = –9
(–9, 0)
Let x = 0.
6y – (0) = 9
6y = 9
y =
(0, )

30. Time for some Guided Practice!!!
Graphing Lines Using Intercepts
Time for some
Guided Practice!!!