2 – 3: Quick Graphs of2 – 3: Quick Graphs ofLinear EquationsLinear Equations

Objective:

CA Standard 17: Use the slope – intercept form of a linear equation to graph a linear equation. Use the standard form of a Linear equation to graph linear equations.

If the graph of an equation intercepts the y-axis at (0, b), then the number

b is the y-intercept of the graph.

Graphing equations in Graphing equations in slope – intercept form.slope – intercept form.

The slope intercept form of an equation gives you a quick way to graph the equation.

Step 1. Write the equation in slope – intercept form by solving for y.

Step 2. Find the y-intercept and use it to plot the point where the line crosses the y-axis.

Step 3. Find the slope and use it to plot a second point on the line.

Step 4. Draw a line through the two points.

Example 1: Graphing with the Slope – intercept form.

Graph 3 4 8x y Step 1: Write the equation in slope – intercept form by solving for y. 3 4 8

4 3 8

32

4

x y

y x

y x

Step 2: Find the y-intercept and use it to plot the point where the line crosses the y-

axis.

The y-intercept is (0, -2). Plot (0, -2)

Step 3: Find the slope and use it to plot a second point on the line.

The slope is ¾. From the point (0, -2) go up 3 units and over to the right 4 units. (4,

1)

Step 4: Draw a line through the two points (0, -2) and (4, 1).

2

-2

-5 5

(4, 1)

(0, -2)

Standard FormStandard Form of a of a Linear EquationLinear Equation

The standard form of a linear equation is

Ax + By = C

where A and B are not both zeros.

Graphing Equations in Graphing Equations in Standard FormStandard Form

The standard form of an equation gives you a quick way to graph the equation:

Step 1: Write the equation in standard form.

Step 2: Find the x-intercept by letting y = 0 and solving for x. Use the x-intercept to plot the point where the line crosses the x-axis.

Step 4: Draw a line through the two points.

Step 3: Find the y-intercept by letting x = 0 and solving for y. Use the y-intercept to plot the point where the line crosses the y-axis.

Example 3: Draw Quick Example 3: Draw Quick GraphsGraphs

Graph 2x + 3y = 12

Step 1: The equation is already in standard form.

Step 2: 2x +3y = 12, let y =0

2x + 3(0) = 12

2x =12

x = 6The x-intercept is (6, 0)

Step 3: 2(0) + 3y = 12, let x = 0

3y =12

y = 4

The y-intercept is (0, 4)

Step 4:

Plot the two points (6, 0) and (0, 4), then draw a line through them.

4

2

-2

-5 5 (6, 0)

(0, 4)

Horizontal and Horizontal and Vertical LinesVertical Lines

Horizontal Lines: The graph of y = c is a horizontal line through (0, c).

Vertical Lines: The graph of x = c is a vertical line through (c, 0).

C is a constant.C is a constant.

HOMEWORKHOMEWORK

P. 86 #25-35 Odd, #43-51 EOO

Example 4:Example 4: Graphing Horizontal Graphing Horizontal and Vertical Linesand Vertical Lines Graph y = 3 and x = -2

2

-2

-5 5

x = -2

y = 3

Example 2: Using the Example 2: Using the Slope – Intercept FormSlope – Intercept Form

To buy a $ 1200 stereo, you pay a $200 dollar deposit and then make weekly payments according to the equation a = 1000 – 40t,

where a is the amount you owe and t is the number of week.

a. How much do you originally owe?

1200 – 200 = 1,000

b. What are your weekly payments?

0 1000 40

40 1000

100025 the amount of your

40weekly payments will be $40 and the

number of weeks will be 25.

t

t

t

c. Graph the model

1000

500

-500

-5 5(25, 0)