Graphing Linear Equations
4A
To graph a line (linear equation), we first want to make sure the equation is in slope intercept form
(y=mx+b). We will then use the slope and the y-intercept to graph the line.
Slope (m): Measures the steepness of a non-vertical line. It is sometimes refereed to as the rise/run
or
. It’s how fast and in what direction y changes compared to x.
y-intercept: The y-intercept is where a line passes through the y axis. It is always stated as an
ordered pair (x,y). The x coordinate is always zero. The y coordinate can be taken from the “b” in
y=mx+b.
Graphing The Linear Equation:
y = 3x - 5
1) Find the slope:
m=3m= 3 . = y .
1
x
2) Find the y-intercept: x = 0 , b = -5  (0, -5)
3) Plot the y-intercept
4) Use slope to find the next point: Start at (0,-5)
m = 3 . = y .  up 3 on the y-axis
1
x
 right 1 on the x-axis
(1,-2) Repeat: (2,1) (3,4) (4,7)
5) To plot to the left side of the y-axis, go to y-int. and
do the opposite. (Down 3 on the y, left 1 on the x)
(-1,-8) Repeat: (-2,-11) (-3,-14)
6) Connect the dots.
Do Now on GP:
1) y = 2x + 1
2) y = -4x + 5
3) y = ½ x – 3
4) y = - ⅔x + 2
Finding the equation of a line in slope intercept form (y=mx + b)
Example: Find the equation in slope intercept form of the line formed by (3,8) and (-2, -7).
Step 1: Find the slope (m):
y y 2  y1
m=

x x 2  x1
(7)  (8)
m=
(2)  (3)
 15
m=
3
III.
Step3: Write Equation
m = 3, x = 3, y = 8
m = 3, b = -1
y = mx + b
y = mx + b
(8) = (3)(3) + b
8=9+b
-9 -9
-1 = b
m=3
m=
Step 2. Use m and one point to find b:
y 3  up3 

 
x 1  right1 
y = 3x - 1
Step 4: Graph
First point = (0,b) = (0, -1)
Special Slopes
A. Zero Slope
* No change in Y
* Equation will be Y =
* Horizontal Line
B. No Slope (undefined slope)
* No change in X
* Equation will be X =
* Vertical Line
Practice Problems: Find the equation in slope intercept form: On some problems , the slope (m) is
given, so you only have to find the y-intercept (b).
1) (-4, -7)(3, 7)
2) m = ¾ , (-8,-9)
3) (4, -7)(-2, 11)
4) (-2, 9)(2, 9)