Linear Equations and Special Cases

Linear Equations and Special Cases - MAC1105 Linear...

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MAC1105: Linear Equations and Special Cases If we are given two data points (or one data point and slope) that are part of a linear relationship, there are several procedures for deriving a linear equation of form y b mx = + = + = + = + or y mx b = + = + . Suppose we are given two data points, (3,2) and (5,14) . We first compute the slope: y 14 2 12 m 6 x 5 3 2 - = = = = - triangle triangle . Note that if we had been given a point and a slope, we would begin at this point. Now that we know the slope there are two ways to finish deriving the equation. 1) We now know that m 6 = , so we have the equation y b 6x = + = + . Substitute into this equation values from a data point and solve for the unknown b as follows. y b 6x (14) b 6(5) 14 b 30 b 16 = + = + = + = - = . We have derived the equation y 16 6x = - + . 2) Plug either data point and the slope into the point-slope formula 1 1 y m(x x ) y = - + . y 6(x 5) 14 y 6x 30 14 y 6x 16 = - + = - + = - . --------------------------------------------------------------------------------------------------------------------------------------- 1) Lines that pass through the origin. Lines whose graphs pass through the origin (0,0) have a y-intercept = 0, so the equations of these lines are very simple, y mx = .
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