<p> Linear Equations/Inequalities By Mrs. Lenora Nelson 1/05/09 From www.freewebs.com/mrs--nelson Plot these two equations: y  5 in green y = # is always a horizontal line</p><p> y=5 x  5 in blue x = # is always a vertical line</p><p>(0, 5) (12, 5)  y = 5 slope = 0</p><p>(5, 3) (5, -7)  x = 5 slope = undefined x=5</p><p>These are the formulas for linear equations.</p><p> y  y y2  y1 y1  y2 y point-slope form: y  y  m(x  x ) slope: m  m  m  m  1 1 x  x x2  x1 x1  x2 x parallel slope: has the same slope of given line Ax  By  C standard form: perpendicular slope: has negative reciprocal slope of given line. A  0 & no fractions slope-intercept form: y  mx  b (y-intercept form) Solution Descriptions Problems generated by http://www.easyworksheet.com All rights reserved. Copyright 1998 Triple Threat Inc. Problem a: Write the equation of the line in standard form Original problem: Line going through (-3,4) and (-4,-2)</p><p>Step 2: Find the slope 4  2 Step 2: m   6 Step 3: Use the point-slope formula  3  4 y  4  6(x  3) Step 3: Step 4: Write in standard form: x&y same side, x positive, no fractions. y  4  6x 18</p><p>Step 4: 6x  y  22 Problem b: Write the equation of the line in standard form Original problem: slope=7 through (-7,6)</p><p>Step 2: Use the point-slope formula y  6  7(x  7) Step 2: Step 3: Write in standard form: x&y same side, x positive, no fractions. y  6  7x  49</p><p>Step 3: 7x  y  55 Problem c: Write the equation of the line in slope-intercept form Original problem: Parallel to line:  3x  5y  1 going through (-4,-5)</p><p> A 3 Step 2: Find slope of given line. Step 2: in standard form m  so m   B 5</p><p> y  5   3 (x  4) Step 3: Use the point-slope formula 5 Step 3:  3 12 y  5  x  5 5 Step 4: Solve for y to get into slope-intercept form. 3 37 Step 4: y   x  5 5 Problem d: Write the equation of the line in slope-intercept form Original problem: Perpendicular to line from problem c and going through same point.</p><p>Step 2: Perpendicular slope is the negative reciprocal 3 5 Step 2: m   so  m  5 3 Step 3: Use the point-slope formula y  5  5 (x  4) 3 Step 3: 5 20 y  5  x  3 3 Step 4: Solve for y to get into slope-intercept form. 5 5 Step 4: y  x  3 3 Graphs courtesy of Mrs. Nelson's membership to http://webgraphing.com/index.jsp Copyright © 2004-2009 WebGraphing.com. All Rights Reserved. </p><p>Page ___</p>