Practice with Parallel and Perpendicular Topic Index | Algebra Index | Regents Exam Prep Center

Try the following problems:

 1. .  If the slope of l1 is  ,  and the slope of l2  is , find the value of x. Answer x = 10 Explanation Since the lines are parallel, the slopes are equal. x/4 = (x+5)/6 6x = 4x + 20 2x = 20 x = 10

 2. Is the equation y = 3x + 2 parallel to 2y + 3x = 3?  Explain. Answer No Explanation The slopes of these lines are NOT equal, so they are not parallel. y=3x + 2 has a slope of 3. 2y+3x = 3  (solve for y) y=(-3/2)x + 3/2    has a slope of (-3/2).

 3. .  If the slope of l1 is  ,  and the slope of l2  is , find the value of x. Answer x = 0 Explanation Since the lines are perpendicular, the slopes are negative reciprocals. 8/(x-6) = -(4/3) 24 = -4x + 24 0 = -4x x = 0

 4. Find the slope of a line parallel to a line whose slope is  . Answer -(2/3) Explanation If lines are parallel, the slopes are equal.

 5. Find the slope of the line perpendicular to a line whose slope is  . Answer 3/2 Explanation When lines are perpendicular, the slopes are negative reciprocals.

 6.. Find the slope of a line parallel to the line whose equation is 3y + 2x = 6. Answer -(2/3) Explanation Since the lines are parallel, the slopes are equal. Be sure to solve for y before reading the slope from the equation. 3y + 2x = 6 y = -(2/3) + 2 y = mx + b   so the slope is -(2/3)

 7. Find the slope of a line perpendicular to the line whose equation is 3y + 2x = 6. Answer 3/2 Explanation Since the lines are perpendicular, the slopes are negative reciprocals. Solve the equation for y before reading the slope. 3y + 2x = 6 y = -(2/3)x + 2 The slope of this line is -(2/3). The slope of the perpendicular is 3/2.

 8. Find the equation of the line parallel to the line whose equation is y = -3x + 5 and whose y-intercept is -5. Answer y=-3x-5 Explanation y=-3x+5 has a slope of -3.  Since parallel lines have equal slopes, your slope will be -3. Use the slope-intercept form of an equation. y=mx+b y=-3x+(-5)

 9. Find the equation of the line perpendicular to the line whose equation is 2y - 4x = 7 and whose y-intercept is +5. Answer y = -0.5x + 5 Explanation Solve for y to read the slope. 2y-4x=7 y=2x+7   has a slope of 2. The slope of the perpendicular would be -(1/2) or -0.5 Use the slope-intercept form. y=mx+b y=-0.5x + 5

 10. Find the equation of the line perpendicular to the line whose equation is 2y - 4x = 7 and which passes through the point (1,2). Answer y-2 = -0.5(x-1) y = -0.5x + 2.5 Explanation Solve for y to read the slope. 2y-4x=7 y=2x+7   has a slope of 2. The slope of the perpendicular would be -(1/2) or -0.5 Use the point-slope form. y-y1 = m(x - x1) y-2 = -0.5(x - 1) OR y = -0.5x + 2.5

 Topic Index | Algebra Index | Regents Exam Prep Center Created by Michael Caldwell