Writing Equations of Lines Worksheets with Answer Key - Free Printable

1. The lines are neither parallel nor perpendicular. The slopes are 2 and 5, which are not equal and their product is not -1.

2. The lines are parallel. The first equation has a slope of 6, and the second equation, when solved for y, gives y = 3x - 0.5, which has a slope of 3. Wait, that's not correct. Let's recheck: 6x - 2y = 1 → -2y = -6x + 1 → y = 3x - 0.5. The slopes are 6 and 3, which are not equal. So the lines are neither parallel nor perpendicular.

3. The lines are parallel. The first equation is y = 4, which has a slope of 0. The second equation, 4y = 6 → y = 1.5, which also has a slope of 0. Since both have slope 0, they are parallel.

4. The lines are perpendicular. The first equation has a slope of 1, and the second equation has a slope of -1. The product of the slopes is (1)(-1) = -1, so they are perpendicular.

5. The lines are perpendicular. The first equation has a slope of 3/4, and the second equation has a slope of -4/3. The product of the slopes is (3/4)(-4/3) = -1, so they are perpendicular.

6. The lines are perpendicular. The first equation has a slope of -4/3. The second equation, when solved for y, gives 5y = -4x - 12 → y = -4/5x - 12/5, which has a slope of -4/5. Wait, that's not correct. Let's recheck: 4x + 5y = -12 → 5y = -4x - 12 → y = -4/5x - 12/5. The slopes are -4/3 and -4/5, which are not negative reciprocals. So the lines are neither parallel nor perpendicular.

7. The lines are parallel. The first equation, 2y = 4x - 6, simplifies to y = 2x - 3, which has a slope of 2. The second equation has a slope of 2. Since both have slope 2, they are parallel.

8. The lines are perpendicular. The first equation has a slope of 3, and the second equation has a slope of -3. The product of the slopes is (3)(-3) = -9, which is not -1. So they are not perpendicular. Wait, that's incorrect. The slopes are 3 and -3, and their product is -9, not -1. So they are neither parallel nor perpendicular.