Slopes of Parallel and Perpendicular Lines Objective To

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Slopes of Parallel and Perpendicular Lines Objective: To discover the relationships between the slopes

Slopes of Parallel and Perpendicular Lines Objective: To discover the relationships between the slopes of parallel lines and perpendicular lines.

What type of lines do lines “p” and “q” look like?

What type of lines do lines “p” and “q” look like?

Answer p and q appear to be parallel lines! How can we use mathematics

Answer p and q appear to be parallel lines! How can we use mathematics to be sure they are indeed parallel?

Calculate the slope of each.

Calculate the slope of each.

slope of p = slope of q = =

slope of p = slope of q = =

What do you notice about the slopes of these two lines? • The slopes

What do you notice about the slopes of these two lines? • The slopes are congruent. parallel congruent

Parallel Conjucture: • Two lines are parallel if their slopes are equal. • Recall

Parallel Conjucture: • Two lines are parallel if their slopes are equal. • Recall the definition of parallel lines then write a few sentences describing why it makes sense that parallel lines would have equal slopes.

Are these lines parallel? slope a = slope b = - NO –The slopes

Are these lines parallel? slope a = slope b = - NO –The slopes are not

Are these lines parallel? slope c = slope d = = YES – Slopes

Are these lines parallel? slope c = slope d = = YES – Slopes are

You will be shown the slopes of two lines. Write down whether each pair

You will be shown the slopes of two lines. Write down whether each pair of lines are parallel or not.

1. slope of line r = slope of line s = These lines are

1. slope of line r = slope of line s = These lines are parallel.

3. slope of line t = slope of line u = These lines are

3. slope of line t = slope of line u = These lines are parallel.

4. slope of line t = slope of line u = Not parallel because

4. slope of line t = slope of line u = Not parallel because the slopes are not congruent to each other.

Ex. Determine whether the graphs of y = -3 x + 4 and 6

Ex. Determine whether the graphs of y = -3 x + 4 and 6 x + 2 y = -10 are parallel lines. Step 1: make both equations in the y-intercept form to compare slopes 6 x + 2 y = -10 can be changed to y-intercept form by solving for y

6 x + 2 y = -10 -6 x Subtract 6 x 2 y

6 x + 2 y = -10 -6 x Subtract 6 x 2 y = -6 x -10 2 2 2 y = -3 x - 5 Divide by 2

Step 2: compare the slopes of both equations. The first equation y = -3

Step 2: compare the slopes of both equations. The first equation y = -3 x + 4 has a slope of -3 and the second equation has the same slope of -3 Therefore, the graph of the lines will be parallel.

Practice: Determine whether the graphs are parallel lines (without graphing) 1) 3 x -

Practice: Determine whether the graphs are parallel lines (without graphing) 1) 3 x - y = -5 and 5 y -15 x = 10 2) 4 y = -12 x + 16 and y = 3 x + 4