{"id":411,"date":"2016-04-15T12:00:25","date_gmt":"2016-04-15T19:00:25","guid":{"rendered":"https:\/\/magoosh.com\/praxis\/?p=411"},"modified":"2019-01-30T17:58:13","modified_gmt":"2019-01-31T01:58:13","slug":"praxis-core-math-linear-equation-practice-questions","status":"publish","type":"post","link":"https:\/\/magoosh.com\/praxis\/praxis-core-math-linear-equation-practice-questions\/","title":{"rendered":"Praxis Core Math: Linear Equation Practice Questions"},"content":{"rendered":"

Linear equations are classified as a type of algebra problem in the official Core Math Study Companion, but they behave like function questions<\/a> in many ways. A linear equation is an equation that states the way that two algebraic variables will always behave in relation to each other, even when the values change.<\/p>\n

In other words, linear equations show variables that are dependent on each other\u2014when the value of one variable changes, the other variable\u2019s value will also change. And the changes will be predictable. To give a very simple example, suppose the values of x<\/em> and y<\/em> are connected, so that whenever the value of x<\/em> goes up by 1, the value of y<\/em> also increases by 1. This is pretty predictable, right?<\/p>\n

But even then, there still must be a point at which x<\/em> and y<\/em> intercept<\/em>. This is the point at which x<\/em> is 0. In the equation described in the above paragraph, if y<\/em> is 0 when x<\/em> is also 0<\/em>, than the linear equation would be x<\/em> = y<\/em>. This is because x<\/em> and\u00a0 y<\/em> will always<\/em> have the same value if they intersect at 0 and each number goes up by 1 when the other number increases by 1. You can see how the linear equation of x<\/em> and y<\/em>\u2019s exact equivalency goes up in the following table:<\/p>\n

\"Table1\"<\/a>
\ntable\u00a0for linear equation x = y<\/strong><\/em><\/p>\n

This same relationship could be expressed by drawing a line<\/em> (hence the name linear<\/em> equation) on a coordinate plane:<\/p>\n

\"XY-plane_exmple_blank-1\"<\/a><\/p>\n

graph for linear equation x = y<\/strong><\/em>
\nThe linear equations you\u2019ll come across in Praxis Core Math questions will be a good deal more complicated, of course. A more typical linear relationship might involve y<\/em> increasing by 8 every time x<\/em> increases by 2. 8 is four times as much as 2, so this means that y<\/em> increases 4 times as quickly as x<\/em>.<\/p>\n

So in terms of the inter-related increase of x<\/em> and y<\/em>, y<\/em> = 4x<\/em>. Now if y <\/em>and x<\/em> both meet each other at 0, then y<\/em> = 4x<\/em> would be the correct linear equation. However, on the Praxis Core, the intercept will probably also be more complex than the example above. Let\u2019s say that y<\/em> is 3 when x<\/em> is 0. To add this intercept to y<\/em> = 4x<\/em>, you can rewrite the linear equation as y<\/em> = 4x<\/em> + 3. On the Core Math test, the table for this equation would look like this:<\/p>\n

\"Table2\"<\/p>\n

table\u00a0for linear equation y = <\/strong><\/em>4x<\/em> + 3<\/strong><\/p>\n

And the graph\u00a0for the equation might look something like this:<\/p>\n

\"Coordinate<\/a><\/p>\n

graph for linear equation x = y<\/strong><\/em><\/p>\n

 <\/p>\n

Linear equation practice question, with table<\/h2>\n

\"Table3\"<\/p>\n

Which of the following equations expresses the relationship between\u00a0x\u00a0<\/em>and y\u00a0<\/em>in the table above?<\/p>\n