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GRAPHS OF LINEAR EQUATION
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.
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)
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
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
4
(1,3)
3
2
(0,1)
1
-4 -3 -2 -1 1 2 3 4
-1
-2
-3
-4
GRAPH THIS:
1. (3,4) and (1,2)
2. (0,5) and (6,1)
3. (-2, 5/2) and ( ½ , ¾)
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
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
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
TRY THIS:
 m= 2/4 and b= 2
 m= 1 and b= 3
 y= ¾ x +3
y= ½x + 1
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
TRY THIS
 m=3 and (0,-5)
 m = -3 and (2,4)
 m= 2/3 and (-2,5)

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Graphs of linear equation

  • 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)