03Asketch-intercepts

= X & Y Intercepts Method = toc This method can be used for any linear function with one exception (see notes below).

Recall that we need to plot __two__ points to produce the graph of a straight line.

This method uses the __**x-intercept**__ and the __**y-intercept**__ as the two points.

X & Y Intercepts Method

 * Step 0: ** Draw a set of axes
 * Graph paper is not necessary for a sketch, but keep it neat
 * Put arrows on the end of each axis
 * Label each axis with **X** and **Y**


 * Step 1: ** Find the x-intercept by making **y = 0** then solve for x.


 * Step 2: ** Plot the x-intercept as a point on the x-axis.


 * Step 3: ** Find the y-intercept by making ** x = 0 ** then solve for y.


 * Step 4: ** Plot the y-intercept as a point on the y-axis.


 * Step 5: ** Rule a line through the two points.
 * Continue the line out to the edge of the graphing area.

** Example 4 **
math \text{Use the X&Y Intercept Method to sketch : } 3x + 2y = 12 math

__**Solution:**__

**1: x-intercept: Make y = 0**

math \\ . \qquad 3x+2y = 12 \qquad \{ \textit{Let } y = 0 \} \\ \\ . \qquad 3x+0 = 12 \\ \\ . \qquad 3x = 12 \qquad \{\div 3 \} \\ \\ . \qquad x = 4 math

**2: Plot x-intercept at** ** (4, 0) **

**3: y-intercept: Make x = 0**

math \\ . \qquad 3x+2y=12 \qquad \{ \textit{Let } x = 0\} \\ \\ . \qquad 0 + 2y = 12 \\ \\ . \qquad 2y = 12 \qquad \{ \div 2 \} \\ \\ . \qquad y = 6 math

**4: Plot y-intercept at (0, 6) **


 * 5: Rule line through two points. **