Kelly's+Notes+-+General+Form+of+Direct+and+Partial+Variations

Skill: State the general form of direct and partial variation. Identify all varia bles

DIRECT VARIATION:

A relationship between two variables in which one variable is a constant multiple of the other , that means if y is always twice as much as x , then they directly vary . For example:


 * ** x ** || ** y ** ||
 * 1 || 2 ||
 * 2 || 4 ||
 * 3 || 6 ||
 * 4 || 8 ||
 * 5 || 10 ||
 * 6 || 12 ||

Here **y** is a constant multiple of **x.** **y**= 2 ** x **

If y varies directly as x, we mean that the ratio between these variables is constant. **If y varies as x then y=kx, where k is the constant of variation**. If y ou graph this relationship,  the  line go es  through the origin (0, 0) and its  slope is called the constant of the variation. That's because each of the variables is a constant multiple of the other. The constant of variation is sometimes called the constant of proportionality.  <span style="font-family: Cambria; mso-bidi-font-family: 'Segoe UI'; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: 'Malgun Gothic'; mso-fareast-language: KO;">
 * The line goes through the origin ||

PARTIAL VARIATION A relationship between 2 variables in which one variable is a constant multiple of the other; plus some constant. **For example: If y varies partially as x, then the equation will be y=kx+b, where k is the constant of variation and b is a fixed value.** If //y// varies partially as //x// the graph is a straight line that does not pass though the origin(0,0). <span style="font-family: Cambria; font-size: 10pt; mso-bidi-font-family: Verdana; mso-fareast-language: KO;"> An example of a partial variation question is: A salesman earns $1,000.00/month plus 8% of total sales. Hence if he sells $50,000 worth of product in a month his earnings are $1,000.00 + 0.08 × $50,000.00 = $5,000.00. This is an example of partial variation. H is salary is composed of a fixed  amount ($1,000.00) and a  variable  amount (8% of total sales).
 * The line does not pass through the origin (0,0) ||

Skill: Interpret domain and range to decide whether the points on a graph should be joined. Interpret domain and range to decide whether the points on a graph should be joined. The points on a graph can be joined when x=r, when r is a real number. <span style="font-family: Cambria; mso-ansi-language: EN-US; mso-fareast-font-family: 'Malgun Gothic'; mso-fareast-language: KO;"> T he line show s graphical values  between the points <span style="font-family: Cambria; mso-ansi-language: EN-US; mso-fareast-font-family: 'Malgun Gothic'; mso-fareast-language: KO;">. <span style="color: #ff0080; font-family: Cambria; font-size: 10pt; mso-bidi-font-family: 'Gill Sans MT'; mso-fareast-font-family: 'Malgun Gothic'; mso-fareast-language: KO;"> <span style="font-family: Cambria; mso-bidi-font-family: 'Gill Sans MT'; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: 'Malgun Gothic'; mso-fareast-language: KO;">Y <span style="font-family: Cambria; mso-bidi-font-family: 'Gill Sans MT'; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold;">ou join dots only if there are values in <span style="font-family: Cambria; mso-bidi-font-family: 'Gill Sans MT'; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: 'Malgun Gothic'; mso-fareast-language: KO;"> <span style="font-family: Cambria; mso-bidi-font-family: 'Gill Sans MT'; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold;">between them **<span style="font-family: Cambria; font-size: 10pt; mso-bidi-font-family: 'Gill Sans MT'; mso-fareast-font-family: 'Malgun Gothic'; mso-fareast-language: KO;">. **<span style="font-family: Cambria; mso-bidi-font-family: 'Gill Sans MT'; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: 'Malgun Gothic'; mso-fareast-language: KO;">For example: x=1 and x=2 <span style="font-family: Cambria; mso-bidi-font-family: 'Gill Sans MT'; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold;">you can <span style="font-family: Cambria; mso-bidi-font-family: 'Gill Sans MT'; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold; mso-fareast-language: KO;">’ <span style="font-family: Cambria; mso-bidi-font-family: 'Gill Sans MT'; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold;">t join <span style="font-family: Cambria; mso-bidi-font-family: 'Gill Sans MT'; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold; mso-fareast-language: KO;"> them <span style="font-family: Cambria; mso-bidi-font-family: 'Gill Sans MT'; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold;"> because there are no values between <span style="font-family: Cambria; mso-bidi-font-family: 'Gill Sans MT'; mso-bidi-font-size: 10.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: 'Malgun Gothic'; mso-fareast-language: KO;">. However you can join them if x=1-2, because 1-2 includes all the values in between 1 and 2 (eg.1.2, 1.3, 1.4)
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