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Take Out Paper for Notes!
Graphs and Linear Equations
What do you remember about…
On a number line, each point is the graph of a
number.
On a plane, each point is the graph of an ordered
pair.
Where would place the
following?:
x-axis
Origin
y-axis
Quadrants
Rene’ Descartes
• French Mathematician and
Philosopher
• Use a coordinate system to combine
algebra and geometry
• Laid the foundation for analytic
geometry
Find 3 points that satisfy the following
conditions:
• The x-coordinate is the
same as the y-coordinate
• (
) (
) (
• The absolute values of the
x-coordinate and the y
coordinate are the same
• (
) (
) (
• The product of the
coordinates is 2
• (
) (
) (
)
)
)
Equations whose graphs are lines
are called linear equations.
• Linear
• Non-Linear
y  2x 1
y  3 x  2
5 y  4
9 x  15 y  7
y  2x2  1
x  y  16
2
y
x
xy  3
2
2
The solution of an equation with two
variables is an ordered pair of numbers,
which can be plotted on a coordinate
plane.
A graph of an equation is
a drawing that represents
its solutions.
So…….. How many ways can we graph?
Ways to graph…
1. T-table
2. Intercepts ( Using x and y
intercepts)
3. Slope – Intercept ( Using the slope
and y-intercept)
4. Point-Slope ( Using one point and
the slope)
T-table
Example 1:
y  3x  2
T-table
• Example 2: 2 x  5 y  10
T-table
• Example 3: y  1 x  1
2
Now it’s your turn….
HIT OR MISS….
Graphing by Intercepts
• This method uses 2 very specific
points on the graph.
• x-intercept- point where the
graph intersects the x-axis
• y-intercept- point where the
graph intersects the y-axis
How do you find intercepts?
• x-intercept…
From the given equation,
let y = 0 , then solve for x.
2 x  5 y  10
Let y  0  2 x  5(0)  10
 2 x  10
x-intercept : (5,0)
 x5
How do you find intercepts?
• y-intercept…
From the given equation,
let x = 0 , then solve for y.
2 x  5 y  10
Let x  0  2(0)  5 y  10   5 y  10  x  2
y-intercept : (0,-2)
Example 4:
6

 ,0
7

 0, 3
7x  2 y  6
Example 5:
 3, 0 
 0, 4 
1
1
x  y 1
3
4
Your turn ….
MESSAGE IN CODE…
GRAPH BY INTERCEPTS