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### 1-3 Graph Linear Functions

### To graph a line 1)using the x and y intercept

Graph linear equations

Find the x and y intercepts of a line

Find the slope of a line through 2 points

Find the zeros of linear functions

Vocabulary

- Independent variable- in a function, the variable whose values make up the domain
- Dependent variable-the variable in a function whose values depend on the domain

Substitute 0 for y to find the x intercept. Then

Substitute 0 for x to find the y-intercept.

Lets look at Example 1 page 22

Example 1

Graph 4x + 3y - 5 = 0 using x- and y-intercepts.

Substitute 0 for y to find the x-intercept. Then substitute 0 for x to find the y-intercept

The line crosses the x-axis at (5/4, 0) , and the y-axis at

. Graph the intercepts and draw the line(0, 5/3).

The slope of a non-vertical line is the ratio of the change in the ordinates(Y-coordinates) of the points to the corresponding change in the abscissas( x-coordinates)

the slope, m, of line through (x1,y1) and (x2 , y2) , if x2≠y2

m = y2-y1

x2-x1

Let’s look at example 2 on page 31

=

Example 2

ENTERTAINMENT The number of U.S. commercial radio stations that play primarily top 40 music has increased from 318 in 1995 to 474 in 2002. What was the average rate of increase in the number of top 40 radio stations

The average rate of change is the slope of the line containing the points at(1995, 318) and (2000, 474). Find the slope of the line.

m = y2-y1

x2-x1

= or about 22.29

On average, the number of top 40 radio stationsincreased by about 22 stations per year from 1995to 2002.

If a line has a slope m and y intercept b, the slope intercept form of the equation of the line can be written as y= mx + b

If the equation is in standard form Ax + By = C then

m = - A/B and b = C/B

Lets look at example 1 on page 36

Example 3

Graph each equation using the y-intercept and the slope.

a. y = -x - 1

The y-intercept is -1. Graph (0, -1).Use the slope to graph a second point.Connect the points to graph the line

b. 2x - 5y = 10

Rewrite the equation in slope-intercept form

The y-intercept is -2. Graph (0, -2). Then use the slope to graph a second point. Connect the points to graph the line

Values for which f(x) -0 are called the zeros of the function f.

For a linear function, the zeros can be found by solving the equation mx + b = 0

Lets look at pg 23 Example 2

To find the zeros of f(x), set f(x) equal to 0 and solve for x.### Example 4Find the zero of each function. Then graph the function.a. f(x) = 2x - 3

2x-3=0 so x=3/23/2 is a zero of the function. So the coordinates of one point on the graph are . Find the coordinates of a second point. When x = 0, f(x) = 2(0) - 3, or -3. Thus, the coordinates of a second point are (0, -3).

b. f(x) = 1

Since m = 0 and b = 1, this function has no x-intercept, and therefore no zeros. The graph of the function is a horizontal line 1 unit above the x-axis.

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