1. 2.3 Graph Equations of Lines

2. In this lesson you will:
Use the slope intercept form of a linear equation to graph linear equations.
Use the standard form of a linear equation to graph linear equations.

3. It gives us a way to locate points (or sets of points) in the plane.
Remember the Cartesian Coordinate system? It is also sometimes called The Rectangular Coordinate System.
y-axis 10
Quadrant II 8
Quadrant I 6 4
Origin 2
-10 -8 -6 -4 -2 O 2 4 6 8 10
x-axis -2 -4
Quadrant III
Quadrant IV
y-coordinate -6 -8
(10,-8)
x-coordinate
It gives us a way to locate points (or sets of points) in the plane.

4. Slope-Intercept Form
If the graph of the equation “crosses the y-axis” at the point (0,3), we say the y-intercept is 3.
If the graph intersects the y-axis at the point (0,b) we say the y-intercept is b.
To find the y-intercept of a line, let x = 0 and solve for y.
The slope intercept form of a linear equation y = mx + b has slope m and y-intercept b.
Notice the line to the right has an x-intercept of (-2,0).

5. Graph the line First, locate the y-intercept -2.
From that point, move 3 units up (change in y) and then 4 units right (change in x).
Draw the line.

6. In addition to the slope-intercept form for the equation of a line, there are other forms too.

7. Forms of a Linear Equation
Standard Form:
Ax + By = C,
Where A, B, and C are real numbers and A and B are not both zero.
Find the values A, B, and C for the next linear equations:
4x + 3y = 6
2x = 7y -1
.75y – 2x = 1
-7y -7y
y – 2x = 1 3 4
A= 4
(4)
A= 2
B= 3
2x – 7y = -1
B= -7
C= 6
3y – 8x = 4
C= -1
(-1)
-8x + 3y = 4
3x - 6y = 5
x + y = 2 1 4 3
8x -3y = -4
A= 3
A= 8
x + y = 2 1 4 3
B= -6
(4)
B= -3
C= 5
C= -4
3x + y = 8
A= 3
B= 1
C= 8

8. Find the x-intercept and y-intercept of the following equation and use the intercepts to graph it:
4x + 2y = 8
y- intercept:
x- intercept: 4 2 6 -2 -4 -6 8 10 -8
-10 x y
Let’s make x= 0;
Let’s make y= 0;
4( ) + 2y = 8
4x+ 2( ) = 8
4x = 8
(0, 4)
2y = 8
(2,0)
x = 2
y = 4
(0, 4)
(2,0)

9. Find the x-intercept and y-intercept of the following standard form equation and use the intercepts to graph it:
6x - 3y = 18
y- intercept:
x- intercept: 4 2 6 -2 -4 -6 8 10 -8
-10 x y
Let x= 0;
Let y= 0;
6( ) - 3y = 18
6x -3( ) = 18
6x = 18
-3y = 18
(3,0)
x = 3
y = -6
(0, -6)
(3,0)
(0, -6)

10. Change the equation to standard form then find the x-intercept and y-intercept and use the intercepts to graph it:
y - x = 1 1 5
y - x = 1 1 5
(5) 4 2 6 -2 -4 -6 8 10 -8
-10 x y
(-1)
y – 5x = 5
5x – y = -5
(0, 5)
y- intercept:
x- intercept:
(-1,0)
Let’s make x= 0;
Let’s make y= 0;
5( ) - y = -5
5x - ( ) = -5
5x = -5
- y = -5
x = -1
y = 5
(0, 5)
(-1,0)

11. Finally, notice
The equation of Horizontal lines have the form y = c
The equation of Vertical lines have the form x = c.
y = 4
x = -3