Finding The Slope of a Linea Equation Some forms of linear equations • Standard Form ax + by = c where a, b, and c are numbers and x and y are variables • Slope-intercept form y = mx + b where m is the slope and b is the y-intercept and x and y are variables How do you find the slope in standard form? • m = -a/b • Example 1 – 4x + 2y = 6 m = -4/2 = -2 • Example 2 – -6x – 2y = 3 m = 6/-2 = -3 For you to try Find the slope of the line whose equation is -10x + 2y = 4 Solution m = 10/-2 = -5 So, the slope of the line is -5 How to find the slope of a line in slopeintercept form • The slope is always the coefficient of x when the equation is in slope –intercept form • Example 1 – y = 5x – 1 m=5 • Example 2 – y = -3/5 x + 7 m = -3/5 What if the equation is not in either form? • When an equation is not in either form, rearrange the terms so that it is in either standard form or slope-intercept form Example 1 – 5x = -2y + 4 Change the equation to standard form by Examples Example 1 – 5x = -2y + 4 Change the equation to standard form by bringing “y” to the same side as “x” using inverse operations 5x = -2y + 4 +2y +2y 5x + 2y = 4 So, m = -5/2 More examples • Example 2 – -4y – 3x = 2 Rearrange the “x” and “y” terms so that the equation is in standard form -3x – 4y = 2 m = 3/-4 For you to try • Find the slope of the line 2x – 4y – 1 = 6 Hint: What can you do to put this equation in standard form? Solution 2x – 4y – 1 = 6 Add 1 to both sides so that the equation is now in standard form 2x – 4y – 1 = 6 +1 +1 2x – 4y =7 m = -2/-4 = 1/2 Notes • Parallel lines have the same slope • The slopes of perpendicular lines are the opposite of the reciprocals of each other Ex/ if lines c and d are perpendicular to each other and the slope of line c is 4, then the slope of line d is -1/4 Notes continued Ex2/ if lines e and f are perpendicular to each other and the slope of line e is -2/3, then the slope of line f is 3/2