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 ntequ2.gif (849 bytes) 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.



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