Quick Review 5-2

Unit 5 - Objective 2 - Graphs or Linear Equations

To graph a linear equation, you can plot two points in order to sketch it. The x and y intercepts are often the easiest two points to determine and use when graphing a linear equation.

Example:

3x + 2y = 12
If x = 0 then solve for y
3 (0) + 2y = 12
2y = 12
y = 6
So the y-intercept is (0, 6)

If y = 0 then solve for x
3x + 2 (0) = 12
3x = 12
x = 4
So the x-intercept is (4, 0)

Now we can graph the points

This line represents the linear equation 3x + 2y = 12

All the points on the line satisfy the equation and all points satisfying the equation are on the line.

The slope, m, of a straight line is the measure of its steepness with respect to the x-axis. If (x₁, y₁) and (x₂, y₂) are two different points on a line, then the slope of the line is defined as:

m = (y₂ - y₁) / (x₂ - x₁) (provided x₂ - x₁ 0)

The slope is referred to as the "rise over the run" or rise/run. The rise means vertical change and run means horizontal change, left to right. Solving an equation for y puts it in y=mx+b form where the slope is the coefficient of x.

Examples:

3x + 2y = 12
(Get y on one side)
2y = -3x + 12
y = -3x/2 + 12/2
y = -3x/2 + 6

We know that -3/2 is the slope and (0, 6) is the y-intercept. So -3 is the rise and 2 is the run. Because this equation is in the form y = mx + b where b is the y-intercept and m is the slope we can now graph the linear equation.