Nursing Entrance Exam

Nursing Preparation Study Guide

√ 3.5.7 Linear Equations A linear equation is an equation made up of two expressions set equal to each other. All linear equations will include: • One or two variables (usually x and y ) • No variable in the equation can be raised to a power greater than 1 • The variable cannot be the denominator of a fraction Examples of Linear Equations: = 3 + 2, = 4, = − < 8 Examples of Non-Linear Equations: = 2 8 , = < , = } Linear equations describe the relationship between an independent (x) and dependent variable (y). We typically write linear equations in slope-intercept form, better known as = + . The variable represents the slope of the function. The slope tells us the rise over the run or may units we must move up/down and left/right to get from one point on our line to the other. The variable represents the y-intercept or the point where the line touches the y-axis. The graphs of linear equations will always be a solid straight line. To determine how to graph a linear equation you can make a table from the equation. Choose values of x , substitute them into the equation, and solve for y . These x and y values will be used to make the ordered pairs. Next, plot these ordered pairs on the coordinate plane and then connect your dots. Remember a line will extend infinitely at both end points. Example Graph = −2 + 4 = −2 + 4 Ordered Pair 0 = −2(0) + 4 = 0 + 4 = 4 4 (0,4) 1 = −2(1) + 4 = −2 + 4 = 2 2 (1,2) 2 = −2(2) + 4 = −4 + 4 = 0 0 (2,0) 3 = −2(3) + 4 = −6 + 4 = −2 −2 (3, −2)

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