Slope for Parallel and Perpendicular Lines (3.10.5)

Question 1

• Two lines are parallel when they have the same slope and different y-intercepts.

Answer 1

• Two lines are parallel when they have the same slope and different y-intercepts.

Question 2

• Two lines are perpendicular when their slopes are the negative reciprocals of each other. Another way to say this is that two lines are perpendicular when the product of their slopes is –1.

Answer 2

• Two lines are perpendicular when their slopes are the negative reciprocals of each other. Another way to say this is that two lines are perpendicular when the product of their slopes is –1.

Question 3

When two lines are parallel, they have exactly the same angle of tilt. They have exactly the same slope with different x-and y-intercepts.

All lines parallel to these two lines will have the same slope with unique x- and y-intercepts.

Answer 3

When two lines are parallel, they have exactly the same angle of tilt. They have exactly the same slope with different x-and y-intercepts.

All lines parallel to these two lines will have the same slope with unique x- and y-intercepts.

Question 4

When two lines are perpendicular, they tilt opposite to each other. And, they exactly reverse how their x’s and y’s change. In this case, every time y changes 3 on the top line, x will change 3 on the second line. And, every time x changes 4 on the top line, y will change 4 on the second line.

Answer 4

When two lines are perpendicular, they tilt opposite to each other. And, they exactly reverse how their x’s and y’s change. In this case, every time y changes 3 on the top line, x will change 3 on the second line. And, every time x changes 4 on the top line, y will change 4 on the second line.

Question 5

You’ve just learned that parallel lines have the same slope. And this gives you a point on the second line. That’s all you need.

Answer 5

You’ve just learned that parallel lines have the same slope. And this gives you a point on the second line. That’s all you need.

Question 6

Your first step is to determine the slope of the parallel line.

Answer 6

Your first step is to determine the slope of the parallel line.

Question 7

Your second and last step is to substitute the coordinates of the point you were given on the parallel line into the
point-slope form of an equation. And, there is your equation!

Answer 7

Your second and last step is to substitute the coordinates of the point you were given on the parallel line into the
point-slope form of an equation. And, there is your equation!

Question 8

Use the same steps here as you did above, only this time the slopes are the negative reciprocals of each other:

1. Find the slope of your equation: m = –1.
2. Determine the slope of the perpendicular line:
   m = +1.
3. Substitute into the point-slope form.
4. Do the arithmetic to get to the
   simpler slope-intercept form of the equation.

Answer 8

Use the same steps here as you did above, only this time the slopes are the negative reciprocals of each other:

1. Find the slope of your equation: m = –1.
2. Determine the slope of the perpendicular line:
   m = +1.
3. Substitute into the point-slope form.
4. Do the arithmetic to get to the
   simpler slope-intercept form of the equation.