Parallel Lines = Lines in the same plane that never intersect. Review: Slope-Intercept form: y = mx+b
Write an equation in slope-intercept form for both of the lines below….what do you notice? y = ⅔x + 5 y = ⅔x - 3
Parallel Lines have the SAME slope and DIFFERENT y-intercepts. To determine whether lines are parallel, you just compare the slopes and the y-intercepts… If slopes are the same and different y-intercepts – the lines are parallel If slopes are the same and the same y-intercepts - you have the same line If slopes are different – the lines are not parallel
1. y = - ⅓x + 5 and 2x + 6y = x + 8y = -24 and y = ¾x - 7
3x + 4y = 12 and y = ½x + 5
1. Identify the slope of the given line 2. Write an equation in Point-Slope form using the identified slope and the given point. y – y 1 = m(x – x 1 ) 3. Convert to Slope-Intercept form (solve for y) y = mx + b
Write an equation in slope-intercept form for the line that contains (8, 2) and is parallel to y = ⅝x - 4
Write and equation in slope-intercept form for the line that contains (2, -6) and is parallel to y = 3x + 9
Perpendicular Lines = Lines that intersect to form right angles (90°)
Write an equation in slope-intercept form for both of the lines below….what do you notice? y = ¾x + 3 y = -(4/3)x + 5
The slopes of perpendicular lines are negative reciprocals of each other. Negative reciprocals: Ex. The negative reciprocal of ½ is -2. The negative reciprocal of -¾ is 4/3.
What is the slope of a line perpendicular to… y = ⅝x + 5 6x + 8y = 24
Are each pair of lines parallel, perpendicular, or neither? y = 3x – 8 and 3x – y = -1
Are each pair of lines parallel, perpendicular, or neither? 9x + 3y = 6 and 3x + 9y = 6
Are each pair of lines parallel, perpendicular, or neither? y = -(5/2)x + 11 and -5x + 2y = 20
Write an equation in slope-intercept form of the line that contains (1, 8) and is perpendicular to y = ¾x + 1.