Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE :Find the slope of the line parallel to y = 3x - 4
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE :Find the slope of the line parallel to y = 3x – 4 The slope of the current line is m = 3 Parallel lines have the same slope so m = 3
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line parallel to 2y + 5x = 8
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line parallel to 2y + 5x = 8 You must solve for y to get the equation into y = mx + b form
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line parallel to 2y + 5x = 8 You must solve for y to get the equation into y = mx + b form
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line parallel to 2y + 5x = 8 You must solve for y to get the equation into y = mx + b form
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line parallel to 2y + 5x = 8 You must solve for y to get the equation into y = mx + b form
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line parallel to 2y + 5x = 8 You must solve for y to get the equation into y = mx + b form Parallel lines have the same slope. So m =
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line perpendicular to
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line perpendicular to Slope of the given line is
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line perpendicular to Slope of the given line is Perpendicular slope - reciprocal ( flip the fraction ) and opposite sign
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line perpendicular to Slope of the given line is Perpendicular slope - reciprocal ( flip the fraction ) and opposite sign m =
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line perpendicular to
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line perpendicular to First solve for y to get equation into y = mx + b form
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line perpendicular to First solve for y to get equation into y = mx + b form
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line perpendicular to First solve for y to get equation into y = mx + b form
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line perpendicular to First solve for y to get equation into y = mx + b form
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line perpendicular to First solve for y to get equation into y = mx + b form m of current line =
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the slope of the line perpendicular to First solve for y to get equation into y = mx + b form m of current line = Flip fraction & change sign
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line parallel to y = - 4x + 3 and thru the point ( 2, 6 )
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line parallel to y = - 4x + 3 and thru the point ( 2, 6 ) Use point – slope formy = m ( x – a ) + b Parallel m = - 4 and the point ( 2, 6 ) becomes our ( a,b )
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line parallel to y = - 4x + 3 and thru the point ( 2, 6 ) Use point – slope formy = m ( x – a ) + b Parallel m = - 4 and the point ( 2, 6 ) becomes our ( a,b ) y = - 4 ( x – 2 ) + 6
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line that runs thru the point ( - 4, 7 ) and is parallel to a line that has a slope of m =
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line that runs thru the point ( - 4, 7 ) and is parallel to a line that has a slope of m = Using point – slope formy = m ( x – a ) + b substitute m and ( a, b )
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line that runs thru the point ( - 4, 7 ) and is parallel to a line that has a slope of m = Using point – slope formy = m ( x – a ) + b
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line that runs thru the point ( 1, - 4 ) and is perpendicular to a line with has a slope of m =
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line that runs thru the point ( 1, - 4 ) and is perpendicular to a line with has a slope of m =
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line that runs thru the point ( 1, - 4 ) and is perpendicular to a line with has a slope of m = ** use point – slope form and substitute m and ( a, b )
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line that runs thru the point ( - 2, - 1 ) and is perpendicular to
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line that runs thru the point ( - 2, - 1 ) and is perpendicular to Solve for y and get into y = mx + b form
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line that runs thru the point ( - 2, - 1 ) and is perpendicular to Solve for y and get into y = mx + b form
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line that runs thru the point ( - 2, - 1 ) and is perpendicular to Solve for y and get into y = mx + b form
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line that runs thru the point ( - 2, - 1 ) and is perpendicular to Solve for y and get into y = mx + b form
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line that runs thru the point ( - 2, - 1 ) and is perpendicular to
Parallel & Perpendicular Lines Parallel Lines – have the SAME slope Perpendicular Lines – have RECIPROCAL and OPPOSITE sign slopes EXAMPLE : Find the equation of the line that runs thru the point ( - 2, - 1 ) and is perpendicular to Solve for y and get into y = mx + b form