This document discusses how to graph linear equations on a coordinate plane using different methods: 1) Using two points from the linear equation to plot and connect those points 2) Using the x-intercept and y-intercept, which are the points where the line crosses the x- and y-axes 3) Using the slope of the line and the y-intercept, where the slope is rise over run and the y-intercept is where the line crosses the y-axis 4) Using the slope of the line and one point from the linear equation Real-world examples of linear equations include stock market trends and car payment plans.

1. GRAPHS OF LINEAR EQUATION

2. WHAT IS A LINEAR EQUATION?
 A linear equation is an
equation whose graph
forms a straight line.
 Linear equations are
usually shown on a
coordinate plane
 Real life situations of
linear equations
include the stock
market as well as the
payments of a car.

3. PARTS OF A COORDINATE
PLANE
Origin
Y-Axis
X-Axis
QUADRANT II
(-x, y)
QUADRANT I
(x, y)
QUADRANT III
(-x, -y)
QUADRANT IV
(x, -y)

4. METHODS IN GRAPHING A LINEAR EQUATION
 Using two points
 Using x- and –y intercepts
 Using the slope and –y intercepts
 Using the slope and a point

5. USING TWO POINTS
Example:
Graph the function:
y = 2x+1
X 0 1
Y 1 3
Substitution:
y =2x+1
y= 2(0)+1
y= 1
y=2x+1
y=2(1)+1
y=3

6. 4
(1,3)
3
2
(0,1)
1
-4 -3 -2 -1 1 2 3 4
-1
-2
-3
-4

7. GRAPH THIS:
1. (3,4) and (1,2)
2. (0,5) and (6,1)
3. (-2, 5/2) and ( ½ , ¾)

8. USING X-INTERCEPT AND Y-
INTERCEPT
 A linear equation
can be graphed by
using x-intercept a
and y-intercept b.
 (a,0) and (0,b) are
enough to graph
linear equation.
 X-intercept- the
abscissa
 Y-intercept- the
ordinate
b
a

9. EXAMPLE:
 y = 3x+2
X 0 -2/3
Y 2 0
Tip: Using this method,
you need to solve for x-
intercept by letting y=0
and y-intercept by letting
x=0 1 2 3
-
1
-
2
-
3
1
2
3
3
2
1

10. USING SLOPE AND Y-INTERCEPT
 In using this method, you need to
identify the slope and the y-
intercept of the linear equation.
 In equation y = 6x+2
m= 6
rise= 6 run= 1
y= 2

11. TRY THIS:
 m= 2/4 and b= 2
 m= 1 and b= 3
 y= ¾ x +3
y= ½x + 1

12. USING SLOPE AND ONE POINT
 To find a point from any equation,
assign any value for x in the given
equation.
Example: In equation y= 2x+1
slope: 2 ordered pair:
(-1,-1)
Let x= -1
y = -1

13. TRY THIS
 m=3 and (0,-5)
 m = -3 and (2,4)
 m= 2/3 and (-2,5)