Horizontal Line

y = 4

In the coordinate plane, the graph of y = 4 is a horizontal line.

From yesterday in case you didn’t get it

x y

3

5

-3

2

-8

4

4

4

4

4

y = # Horizontal Line

Vertical Line

x = 3

In the coordinate plane, the graph of x = 3 is a vertical line.

From yesterday in case you didn’t get it

x y

3

3

3

3

3

-3

5

2

0

-8

x = # Vertical Line

Graph 5x + 7y =35Solve for “y”7y = -5x +35 7 7 7

X -values

Y= -5/7x +5 Y- values

(X, Y)

-7 -5/7(-7)+5 10 (-7, 10)

0 -5/7(0)+5 5 (0,5)

7 -5/7(7)+5 0 (7, 0)

€

y =−5

7x + 5

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 YOUAN EASIER WAY TO GRAPH LINES

BUT REMEMBER WHEN ALL ELSEFAILS, YOU CAN ALWAYS SOLVEFOR 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.

4

3

2

1

-1

-2

-3

-6 -4 -2 2 4 6

A

B

y - intercept

x - intercept

y

X(2,0)

(0,-1)

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).

x - intercept

y - intercept

EXAMPLES OF X-INTERCEPTS

EXAMPLES OF Y-INTERCEPTS

(-2,0)

(-1,0)

(4,0)

(0,0)

(1.8,0)

(-256,0)

(0,-44)

(0,19)

(0,5)

(0,0)

REMEMBER Y = 0

REMEMBER X = 0

(4,0)(0,-3)Make a small t-chart

4

0

0

-3

x y

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

• 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)

(6,0)

(0,3) 4x + 8y =24

6

5

4

3

2

1

-1

-2

-3

-4

-5

-8 -6 -4 -2 2 4 6 8

Graph 4x + 3y = 12 using intercepts

Find x-intercept

4x + 3(0) = 12

Find y-intercept

4(0) + 3y = 12

4x = 12x = 3

3y = 12

y = 4

6

5

4

3

2

1

-1

-2

-3

-4

-5

-8 -6 -4 -2 2 4 6 8

Graph 2x + 3y = 12 using intercepts

x y0

04

6

6

5

4

3

2

1

-1

-2

-3

-4

-5

-8 -6 -4 -2 2 4 6 8

Graph 3x + 5y = 15 using intercepts

x y0

03

5

DO YOU THINK THESE LINES INTERSECT???

6

5

4

3

2

1

-1

-2

-3

-4

-5

-8 -6 -4 -2 2 4 6 8

Graph 5x - 2y = 10 using intercepts

x y0

05

2

6

5

4

3

2

1

-1

-2

-3

-4

-5

-8 -6 -4 -2 2 4 6 8

Graph 2y = 3x - 6 using intercepts

x y0

03

2

-3x + 2y = -6Put into Standardform first:Ax + By = C

Horizontal and Vertical Lines

• The graph of y= # is HORIZONTAL• The graph x =# is VERTICAL

6

5

4

3

2

1

-1

-2

-3

-4

-5

-8 -6 -4 -2 2 4 6 8

Graph 4y = 16 using 3-points

x y

036

4 4

y = 4

6

5

4

3

2

1

-1

-2

-3

-4

-5

-8 -6 -4 -2 2 4 6 8

Graph 3x = 18 using 3-points

x y

03

- 4

x = 6

Warm upsFind the x- and y- intercepts:

1. x – y = 4

2. 2x + 3y = -6

3. 3x + y = -5

4. 4y = 2x – 12

5. y = ½ x + 5

(4,0) (0,-4)

(-3,0) (0,-2)

(-5/3,0) (0,-5)

(6,0) (0,-3)

(-10,0) (0,5)-2x + 4y = -12

-x + 2y = 10

2y = x + 10

Get rid of fraction, multiply everything by 2

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 14x – 6y = 12

Y - intercept:4(0) – 6y = 12 0 – 6y = 12 -6y = 12 y = -2 (0,-2)

X – intercept:

4x – 6(0) = 12

4x – 0 = 12

4x = 12

x = 3

(3,0)Graph on y-axis Graph on x-axis

Example 22x + 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

4. x = 3 SimplifyTo find the y - intercept:

1. Write the original equation. 4x + 3y = 12

2. 4(0) + 3y = 12 Substitute 0 for x

3. 3y = 12 Solve for y

4. y = 4 Simplify

The intercepts are at the points

(3, 0) and (0,4)

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

TOOx – 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?

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)

(20,0)

(0,12)3x + 5y = 60

3x + 5y = 60

3(10) + 5y = 60 30 + 5y = 60 5y = 30 y = 6 (10, 6)

3(15) + 5y = 60 45 + 5y = 60 5y = 15 y = 3 (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