From yesterday in case you didn’t get it
Horizontal Line
x
y
y=4
3
4
5
4
-3
4
2
4
-8
4
In the coordinate plane, the graph of y = 4 is a horizontal
line.
y=#
Horizontal Line
From yesterday in case you didn’t get it
Vertical Line
x
x=3
y
3
-3
3
5
3
2
3
0
3
-8
In the coordinate plane, the graph of x = 3 is a vertical
line.
x=#
Vertical Line
Graph 5x + 7y =35
Solve for “y”
7y = -5x +35
7 7
7
5
y
x 5
7
Y= -5/7x +5
XY(X, Y)
value
values
s
-7
-5/7(-7)+5 10
(-7, 10)
0
-5/7(0)+5
5
(0,5)
7
-5/7(7)+5
0
(7, 0)
Find 3 points using the table, and graph the
line of the equation. y = 2x - 3
-2
-7
-1
-5
0
-3
1
-1
TODAY I AM GOING TO SHOW YOU
AN EASIER WAY TO GRAPH LINES
BUT REMEMBER WHEN ALL ELSE
FAILS, YOU CAN ALWAYS SOLVE
FOR Y AND MAKE A T-CHART!!!
• The x-intercept of a graph is the point
where the graph crosses the x-axis.
• The y-intercept of a graph is the point
where the graph crosses the y-axis.
y
4
3
x - intercept
2
B
1
-6
-4
-2
2
4
X
(2,0)
(0,-1)
-1
y - intercept
-2
A
-3
-4
6
Vocabulary – BIG CONCEPT
x-intercept - the coordinate of a point where the
graph crosses the x-axis. (Important – this is when
y = 0)
y-intercept - the
coordinate of a point
where the graph
crosses the y-axis
(when x = 0).
y - intercept
x - intercept
EXAMPLES OF X-INTERCEPTS
(-2,0)
(0,0)
REMEMBER Y = 0
(-1,0)
(1.8,0)
(4,0)
(-256,0)
EXAMPLES OF Y-INTERCEPTS
(0,-44)
(0,19)
(0,5)
(0,0)
REMEMBER X = 0
:
• To find the x-intercept, plug zero in for y and
solve for x.
• To find the y-intercept, plug zero in for x and
solve for y.
(4,0)
Make a small t-chart
x
y
4
0
0
-3
(0,-3)
So when is it a good idea to use x
and y intercepts to graph???
• When the two coefficients go into the
constant!!
• 2x + 3y = 6
• -3x – 4y = 24
• 12x + 5y = 60
• 5x – 4y = 40
Graph the equation
4x + 8y =24 using the x and y-intercepts.
• Find the x and y-intercepts.
• Plot the x and y-intercepts and draw a line
through them connecting them with a straight
edge.
4x + 8y =24
x-intercept
y-intercept
4x + 8(0) = 24
4(0) + 8y = 24
4x = 24
8y = 24
(6,0)
(0,3)
(0,3)
(6,0)
Identify the x-intercept and y-intercept
of the graph.
Graph 4x + 3y = 12 using intercepts
6
Find x-intercept
5
4x + 3(0) = 12
4x
= 12
x
4
Find y-intercept
4(0) + 3y = 12
3y = 12
3
2
=3
y=4
1
-8
-6
-4
-2
2
-1
-2
-3
-4
4
6
8
Graph 2x + 3y = 12 using intercepts
6
5
4
x
0
y
4
6
0
3
2
1
-8
-6
-4
-2
2
-1
-2
-3
-4
4
6
8
Graph 3x + 5y = 15 using intercepts
6
5
4
x
0
y
3
5
0
3
2
1
-8
-6
-4
-2
2
-1
-2
DO YOU THINK THESE LINES
INTERSECT???
-3
-4
4
6
8
Graph 5x - 2y = 10 using intercepts
6
5
x y
0 5
2 0
4
3
2
1
-8
-6
-4
-2
2
-1
-2
-3
-4
-5
4
6
8
Graph 2y = 3x - 6 using intercepts
Put into Standard
form first:
Ax + By = C
6
x y
0 3
2 0
-3x + 2y = -6
5
4
3
2
1
-8
-6
-4
-2
2
-1
-2
-3
-4
4
6
8
Horizontal and Vertical Lines
• The graph of y= # is HORIZONTAL
• The graph x =# is VERTICAL
Graph 4y = 16 using 3-points
4
46
y=4
5
4
3
2
-8
x
0
3
6
1
y
-6
-4
-2
2
-1
-2
-3
-4
4
6
8
Graph 3x = 18 using 3-points
6
x=6
5
4
3
2
x
-8
-6
y
0
3
-4
1
-4
-2
2
-1
-2
-3
-4
4
6
8
Warm ups
Find the x- and y- intercepts:
1. x – y = 4
(4,0) (0,-4)
2. 2x + 3y = -6
(-3,0) (0,-2)
3. 3x + y = -5
(-5/3,0) (0,-5)
4. 4y = 2x – 12
(6,0) (0,-3)
5. y = ½ x + 5
Get rid of fraction,
multiply everything by 2
-2x + 4y = -12
2y = x + 10
-x + 2y = 10
(-10,0) (0,5)
Graph in Standard Form:
Steps:
1. Find the x- and y- intercepts
2. Graph x-intercept on x-axis (
)
3. Graph y-intercept on y-axis ( )
4. Connect the dots
Example 1
4x – 6y = 12
Y - intercept:
4(0) – 6y = 12
0 – 6y = 12
-6y = 12
y = -2
(0,-2)
Graph on y-axis
X – intercept:
4x – 6(0) = 12
4x – 0 = 12
4x = 12
x=3
(3,0)
Graph on x-axis
Example 2
2x + 4y = -6
Y - intercept:
2(0) + 4y = -6
0 + 4y = -6
4y = -6
y = -3/2
(0,-3/2)
X – intercept:
2x + 4(0) = -6
2x – 0 = -6
2x = -6
x = -3
(-3,0)
Find the x and y intercepts of 4x + 3y = 12
To find the x - intercept:
1. Write the original equation. 4x + 3y = 12
2.
4x + 3(0) = 12
Substitute 0 for y
3.
4x = 12 Solve for x
The intercepts are at the points
4.
x = 3 Simplify
To find the y - intercept:
(3, 0) and (0,4)
1. Write the original equation. 4x + 3y = 12
2. 4(0) + 3y = 12 Substitute 0 for x
3. 3y = 12
4. y = 4
Solve for y
Simplify
Using intercepts, graph the line x – 2 = 4y
Hint: Find the x and y intercepts – then connect
the dots.
Remember – 2 points determine a line!
Using intercepts, graph the line y = -2x + 25
Graph the equation: 2x + 5y = 10
TOO
x – 6y = -6
y-intercept: (0,1)
x-intercept: (-6,0)
6y = -3x + 18
y-intercept: (0,3)
x-intercept: (6,0)
Quick Review
 An x-intercept is the ______ coordinate of a point
where a graph crosses the ____ axis.
 At the x-intercept, the value of y is _____.
 A y-intercept is the ______ coordinate of a point
where a graph crosses the ____ axis.
 At the y-intercept, the value of x is ______ .
 To graph a line using the intercepts you need to…….
 How many ways do you know how to graph NOW?
: You make and sell decorative bows.
You sell small bows for $3 and large bows for $5. You
want to earn $60 per week. This situation can be
modeled by 3x + 5y = 60 where the x is the number of
small bows and y is the number of large bows.
3x + 5y = 60
x-intercept
3x + 5(0) = 60
3x = 60
x = 20
(20,0)
y-intercept
3(0) + 5y = 60
5y = 60
y = 12
(0,12)
(0,12)
(20,0)
3x + 5y = 60
3(10) + 5y = 60 3(15) + 5y = 60
30 + 5y = 60
45 + 5y = 60
5y = 30
5y = 15
y=6
y=3
(10, 6)
(15, 3)
3x + 5(9) = 60
3x + 45 = 60
3x = 15
x=5
(5, 9)
1) 20 Small Bows , 0 Large Bows
2) 0 Small Bows, 12 Large Bows
3) 10 Small Bows, 6 Large Bows
4) 15 Small Bows, 3 Large Bows
5) 5 Small Bows, 9 Large Bows