03Asketch-gradient

= Gradient-Intercept Method = toc

Use this method when the rule is in the form : ** y = mx + c ** {If it isn't, then first rearrange the rule to get it in the form y = mx + c}

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

Also recall that for y = mx + c
 * m = gradient
 * c = y-intercept

Gradient-Intercept 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** : Plot a point at c on the y-axis. {ie at ** (0, c) ** }


 * Step 2: ** Write the gradient as an improper fraction. {If it is a whole number, make the denominator = 1}

The rule for gradient is Compare the gradient from your equation to the rule and get values for ** rise ** and ** run ** {If there is a negative, it belongs to ** rise **}


 * Step 3: ** Starting from the y-intercept, move __up__ the y-axis, by a distance equal to ** rise ** {go __down__ if ** rise ** is __negative__}


 * Step 4: ** From the point in step 3, move to the __right__ by a distance equal to ** run. ** Plot the second point where you end up.


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

** Example 2 **
math \text{Use the gradient-intercept method to sketch : } \; y = \dfrac{3}{4}x + 2 math

media type="custom" key="11977223" __**Solution:**__


 *  **

media type="custom" key="11977235" ... media type="custom" key="11977237" ... media type="custom" key="11977239" ... media type="custom" key="11977241" ... media type="custom" key="11977243" ... media type="custom" key="11977245"

media type="custom" key="11977227" include component="page" wikiName="bhs-methods34" page="zHTML_div_close" {Notice that the gradient gives a line that goes __up__ by ¾ for each step of 1 to the right}

** Example 3 **
math \text{Use the gradient-intercept method to sketch : } \; y = -2x + 3 math


 * __Solution:__**

From the rule:
 * c = 3 {y-intercept at ** (0, 3) ** }
 * m = –2 {gradient}

math \text{Gradient } = \dfrac{-2}{1} math

so {starting at the y-intercept ** (0, 3) ** }
 * rise = –2 {go __down__ 2}
 * run = 1 {go __right__ 1}

{second point at ** (1, 1) ** }