Writing Equations of Parallel Lines (IN REVIEW) You can use the slope m of a nonvertical line to write an equation of the line in slope-intercept form. y = m x + by = m x + b The y -intercept is the y -coordinate of the point where the line crosses the y -axis. slope y- intercept

Writing an Equation of a Line (IN REVIEW) Write an equation of the line through the point (2, 3) that has a slope of 5. SOLUTION y = m x + b 35 3 = 10 + b –7 = b Write an equation. Since m = 5 and b = –7, an equation of the line is y = 5x – 7. Slope-intercept form Substitute 2 for x, 3 for y, and 5 for m. Simplify. Subtract. Solve for b. Use (x, y) = (2, 3) and m = 5. (2) equation of the line is y = 5x – 7

Line n 1 has the equation – x – 1 y = Line n 2 is parallel to n 1 and passes through the point (3, 2). Write an equation of n 2. Find the slope – The slope of n 1 is. Because parallel lines have the same slope, the slope of n 2 is also – Writing an Equation of a Parallel Line (IN REVIEW) SOLUTION

Line n 1 has the equation – x – 1 y = Line n 2 is parallel to n 1 and passes through the point (3, 2). Write an equation of n 2. y = m x + b 2 = –1 + b 3 = b Write an equation. 2 = – (3) + b 1313 Because m = and b = 3, an equation of n 2 is – x + 3 y = 1313 – 1313 – Solve for b. Use (x, y) = (3, 2) and m =. Writing an Equation of a Parallel Line (IN REVIEW) SOLUTION

The slopes of two lines can be used to tell whether the lines are perpendicular. POSTULATE Postulate 18 Slopes of Perpendicular Lines In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1. Lines k 1 and k 2 have the same slope. Slope of Perpendicular Lines k3k3 Line k 3 is perpendicular to k 1 and k 2. Vertical and horizontal lines are perpendicular. 3.7

Deciding Whether Lines are Perpendicular Find the slope of each line. Is j 1  j 2 ? Points on j 1 are (1, 1) and (3, 5). Points on j 2 are (6, 1) and (3, 5) SOLUTION Line j 1 has a slope of m 1 =m 1 = 4242 = 2 Line j 2 has a slope of m 2 =m 2 = 2 Because the product of their slopes is -1 the lines have perpendicular slopes, j 1  j = -1 j2 j2 3.7

Deciding Whether Lines are Perpendicular Decide whether the lines are perpendicular. SOLUTION y = m x + b Multiply the slopes to see if the lines are perpendicular. The product of the slopes is not -1. So, h and j are not perpendicular. Slope-intercept form Rewrite each equation in slope-intercept form to find the slope. line h: 4x + 5y = 2 line j: 5x + 4y = 3 5y = -4 x + 2 4y = -5 x + 3 line h: 4x + 5y = 2 line j: 5x + 4y = 3 y = 10 x slope = m = -4 5 slope = m =