Parallel and Perpendicular Lines
Sketch a graph: y = 2x + 1 b) What is the slope & the y-intercept?
Slope-Intercept Form: y = mx + b Point-Slope Form: Linear Equations Slope-Intercept Form: y = mx + b Point-Slope Form: y – y1 = m(x – x1) m = slope m = slope b = y-intercept (x1,y1) – point that the line goes through
Parallel Lines y = mx + b Parallel Lines have the exact same slope.
1) What is the slope of a line that is parallel to the line y=4x-7?
Write the equation of the line parallel to y = -2x + 1 that has a y-intercept of -4. 4) Write the equation of the line parallel to y = 1/2x – 6 that has a y-intercept of 2.
5) Find the equation of the line parallel to y=3x+6 passing through the point (-1,9).
You try! Write an equation for the lines parallel to the given lines and passing through the given points. 6) y = 1/2x – 4; (4,2) 7) y = -2x + 3; (1,2) 8) y = x – 6; (2,5)
9) Are the lines y = -2x + 4 and 5x + 10y = 3 parallel ?
10) Are the lines 3x + y = 4 and -6x + 2y = -1 parallel?
Perpendicular Lines y = mx + b Perpendicular lines have opposite reciprocal slopes. Also, the product of their slopes is -1.
What is the negative reciprocal of each slope? 1 b) -5 c) 1/3 d) -2/5
1) What is the slope of a line that is perpendicular to the line y=-3x – 7 ?
Write the equation of the line perpendicular to y = -3x + 1 that has a y-intercept of 5.
You try! Write an equation for the lines perpendicular to the given lines and passing through the given points. 6) y = -x + 1; (2,-3) 7) y = 2x + 4; (4,2) 8) y = x – 6 ; (0,-1)
and -3x + 6y = 1 perpendicular ? 9) Are the lines 2x + y = 4 and -3x + 6y = 1 perpendicular ?
10) Are the lines 3x + 4y = 5 and 6x + 8y = -1 perpendicular?