Graphing Linear Equations

Pre-Calculus 411-3

World Population

The population in the world had reached 6 billion in 1999.

The population is expected to reach 7 billion in October of this year.

What is the average rate of increase?

Can you predict the population in 2020.

Graph this linear equation

Linear Equation

Ax + By + C = 0

Solutions of the linear equation are points on the graph

X-intercept

Y-intercept

Example

Graph 3x – y – 2 = 0 using the x- and y- intercepts

Substitute 0 for y to find the x-intercept.

Substitute 0 for x to find the y-intercept

€

−b

m

€

y = −2

The line crosses the x-axis at

€

2

3,0

⎛

⎝ ⎜

⎞

⎠ ⎟ The line crosses the y- axis at (0, -2)

Slope

Ratio of Change

€

m =y2 − y1

x2 − x1

The rate of increase in the world population is the slope of the line you graphed.

Linear Equations

Standard Form

Ax + By = C

Slope- intercept Form Y = mx + b

Question

When is a linear equation not a function?

Hint: see the four types of slopes

When the slope is undefined, vertical line

Zeros of a function

The x-intercepts, solutions

Found when F(x) = 0

0 = mx + b

If m does not equal 0, then solution is

In a case where m = 0, f(x)=b and thus is a constant function, graph is a horizontal line.