Parallel Lines LIVE

Parallel Lines

Objective: Identify parallel lines given equations.

Multiple Choice

Convert the standard form equation into slope-intercept form.

6x - 7y = -35

•  $y=\frac{7}{6}x-5$ 

•  $y=\frac{6}{7}x+5$ 
  

•  $y=\frac{5}{7}x-6$ 
  

•  $y=-\frac{6}{7}x-5$ 

Parallel Lines

Lines side by side and having the same distance continuously between them

VIDEO

Video illustration of the fact that is stated on the next slide.

SLOPE

In the coordinate plane, Parallel Lines have the SAME SLOPE

Multiple Choice

REVIEW: What is the slope of the line:  $y=\frac{2}{3}x+4$  

•  $\frac{2}{3}$  

•  $-\frac{2}{3}$  

•  $\frac{3}{2}$  

•  $4$  

•  $-4$  

SLOPE

In the coordinate plane, Parallel Lines have the SAME SLOPE

Yes its the same slide.

Yes it is here for a reason

Parallel Lines have the SAME SLOPE

Multiple Select

Which two lines are parallel?

• $y=\frac{3}{7}x-25$

• $y=\frac{3}{7}x+2$

• $y=\frac{7}{3}x-25$

• $y=3x+13$

• $y=7x+9$

Multiple Select

Which two lines are parallel?

•  $y=4x-25$ 

•  $y=\frac{1}{4}x+2$ 

•  $y=x-25$ 

•  $y=4x+13$ 

•  $y=-4x+9$ 

What about equations in different forms?

What if one equation is in slope-intercept form.

Like: y = mx + b

And another equation is in point-slope form.

Like: y - y₁ = m(x - x₁)

EXAMPLE 1

Are y = 2x + 4 and y - 19 = 2(x + 21) parallel?

This one is not difficult.

Both forms give us the slope.

EXAMPLE 1 (continued)

Are y = 2x + 4 and y - 19 = 2(x + 21) parallel?

Equation 1: y = 2x + 4

The slope is 2

Equation 2: y - 19 = 2(x + 21)

The slope is 2

BOTH have a slope of 2 so YES they are parallel.

Multiple Select

Which two lines are parallel?

•  $y=-4x-25$ 

•  $y=\frac{1}{4}x+2$ 

•  $y+3=4\left(x-32\right)$ 

•  $y-2=\frac{1}{4}\left(x+67\right)$ 

•  $y+\frac{1}{4}=2\left(x-\frac{1}{4}\right)$ 

But...

What if one equation is in slope-intercept form.

Like: y = mx + b

And another equation is in standard form.

Like: Ax + By = C

Standard Form DOES NOT give us the slope.

We will have to rewrite it to find the slope.

VIDEO

Pay attention when he talks about parallel lines.

He mentions perpendicular lines but we will do that in the next lesson.

EXAMPLE 2

Are y = 2x + 4 and 2x + 4y = 12 parallel?

IMPORTANT: just because there is a 2 in front of each x DOES NOT mean they are parallel. The second equation needs to be rewritten into slope-intercept form. (y = mx + b)

EXAMPLE 2 (cont'd)

Rewrite 2x + 4y = 12 in slope-intercept form.

Overall Goal: get y by itself

Step 1: Subtract the x-term from both sides. (in this case -2x)

Step 2: Divide everything on both sides by the number in front of y

(in this case 4)

EXAMPLE 2 (continued)

Are y = 2x + 4 and 2x + 4y = 12 parallel?

Equation 1: y = 2x + 4

Slope = 2

Equation 2: 2x + 4y = 12 rewritten in slope-intercept form: y = -1/2x + 3

Slope = -1/2

Slopes are NOT THE SAME so they are NOT PARALLEL.

Multiple Choice

Which line is parallel to the line:  $5x+6y=12$  

•  $y=-\frac{5}{6}x-2$  

•  $y=\frac{5}{6}x+13$  

•  $y=5x+11$  

•  $y=-5x-100$  

Multiple Choice

Which line is parallel to the line:  $3x+4y=-24$  

•  $y=-\frac{3}{4}x-1$  

•  $y=\frac{4}{3}x+13$  

•  $y=3x+1$  

•  $y=-3x-10$  

•  $y=\frac{3}{4}x-19$  

Multiple Select

Which lines are parallel to the line:  $5x-8y=32$  

•  $y=\frac{5}{8}x-1$  

•  $y=-\frac{5}{8}x+13$  

•  $y-12=\frac{5}{8}\left(x+13\right)$  

•  $y-5=\frac{5}{8}\left(x+8\right)$  

•  $y-2=-\frac{5}{8}\left(x+3\right)$