Parallel Lines

A line has a slope of -3 and a y-intercept of (0, -1). What is the equation of the line that is parallel to the given line and passes through the point (-3, 1)? A.y = -3x - 8 B.y = 3x + 10 C.y = -3x + 4

A.

The equation of a line is y = -4x + 1. What is the equation of the line that is parallel to the first line and passes through (-2, -1)?

A. y = -4x - 9

A line contains the points (3, 2) and (-1, -6). What is the slope of a line that is parallel to this line?

A. 2

Two lines are parallel. The first line passes through (6, 1), and its y-intercept is (0, -11). Which of the following cannot be the equation of the second line? A.y = 2x + 7 B.2x + y = 6 C.4x - 2y = 2 D.6x = 3y - 2

B

What is the slope of a line that is parallel to 6x + 3y = -9?

C. -2

The coordinates of 3 of the vertices of a parallelogram are (-7, 3), (-6, 1), and (-4, 5). What is the equation for the line containing the side opposite the side containing the first two vertices? (Remember, opposite sides of a parallelogram are parallel.)

C. y=-2x-3

The equation of a line is y = 2x - 1. What is the equation of the line that is parallel to the first line and passes through (-4, 1)?

D. = 2x + 9

A line passes through the point (-3, 4) and its y-intercept is (0, -2). What is the equation of the line that is parallel to the given line and passes through the point (-5, 2)?

D. y=2x-8

You and a friend sign up for a health club. It costs $50 to join, plus $20 a month. However, the first 100 customers can sign up for $30, plus $20 a month. Your friend is customer 100, and you are 101. If the accumulated cost for each membership were graphed, what would it look like? What would the difference be between your accumulated cost and your friend's accumulated cost at any given month?

The graph would be two parallel lines with a slope of 20. One would have a y-intercept of 30, and the other would have an intercept of 50. The graph would be parallel lines because after the inital fee to join, the cost for each is constant each month. The cost will always be $20 different ($50 - $30 = $20) between the accumulated cost of the memberships.

The vertices of a figure are labeled clockwise A(-4, 2), B(2, 4), C(7, 1), and D(-5, -3). How could you show that the figure is a trapezoid? (Hint: A trapezoid has exactly one pair of parallel sides.)

You could plot the points on a coordinate plane to see if the shape was a trapezoid. To prove it, though, you could show that side AB is parallel to side CD by finding that the slope of each side is the same, using the slope formula. Then, you could show that side AD and side BC are not parallel by showing that the slopes are not the same.