Parallel and Perpendicular Lines

Parallel and Perpendicular Lines

A straight line has

• slope

• y-intercept

Slope (m)

• shows steepness of the line

• rise over run between two points

• 
  
   $m=\frac{rise}{run}$  
  

• slope of this line is  $\frac{2}{3}$  

Read the graph from left to right

• Green line has a positive slope

• Red line has a negative slope

Multiple Choice

What is the slope of the line ? Use points C and D and find rise over run.

• $\frac{1}{3}$

• $-\frac{1}{3}$

• $3$

• $-3$

Multiple Choice

What is the slope of the line ? Use points C and D and find rise over run.

•  $-2$  
  

•  $2$ 
  

•  $3$  
  

•  $-\frac{1}{2}$  
  

y-intercept (b)

• is the point where the line crosses the y-axis.

• y-intercept of this line is at (0, -2)

• b = -2

Multiple Choice

What is the y-intercept of the line?

• 1

• 2

• 3

• -3

an equation can represent a straight-line

• slope-intercept form of a line is $y\ =\ mx\ +\ b$  

• so, the equation of this line is  $y=\frac{2}{3}x\ -\ 2$  

Multiple Choice

slope-intercept form of a line is

• $y=mx\ +\ b$

• $y\ -\ y₁\ =\ m\left(x\ -x₁\right)$

• $Ax\ +\ By\ =C$

• $y=m\left(x\ -\ x₁\right)+y₁$

Parallel Lines

• never intersect

• have same slope

• have different y-intercepts

Parallel Lines

• equation of the blue line     $y=\frac{2}{3}x\ +3$  

• equation of the green line    $y=\frac{2}{3}x\ -2$  

• equations have the same slope:   $\frac{2}{3}$ 

Multiple Select

Line w has the equation $y=\ -5x\ +1$   .  Which of the following lines is parallel to line w?  Select all that apply.

•  $y=\frac{1}{5}x\ +\ 3$  

•  $y=-5x\ -4$  

•  $y=-5x+3$  

•  $y=x+5$  

•  $y=-x-5$  

Multiple Choice

Line f has the equation $y=-x\ +\ 3$   .  What is the slope of any line that is parallel to line f?

• -1

• 1

• 3

• x

What if the equation is not in slope-intercept form? like $y\ -\ 2x\ =5$   

• Solve the equation for y

• The slope of the line is +2 not (-2)

Multiple Choice

What is the slope of the line $y+7x=-15$  

• -7

• 7

• -15

• -1

What is opposite of a number?

Change the sign

Multiple Choice

What is opposite of $-\frac{1}{3}$   ?

•  $\frac{1}{3}$  

•  $3$  

•  $-3$  

•  $-\frac{1}{3}$  

What is the reciprocal of a number?

Flip it upside down.

Multiple Choice

What is the reciprocal of 7?

• $\frac{1}{7}$

• $-\frac{1}{7}$

• $7$

• $-7$

Opposite Reciprocal

• change the sign

• flip it upside down

Multiple Choice

What is the opposite reciprocal of $-\frac{4}{5}$   

•  $\frac{4}{5}$  

•  $\frac{5}{4}$  

•  $-\frac{4}{5}$  

•  $-\frac{5}{4}$  

Perpendicular Lines

• intersect each other at a 90 degree angle

• have opposite reciprocal slopes

Perpendicular Lines

• slope of green line is $\frac{2}{3}$   

• slope of blue line is  $-\frac{3}{2}$  

Multiple Choice

Line h and t are parallel. Line w is perpendicular to them. If the slope of line t is

 $-\frac{1}{3}$  what is the slope of line h?

•  $-\frac{1}{3}$  

•  $\frac{1}{3}$  

•  $3$  

•  $-3$  

• Not enough information to tell.

Multiple Choice

Line h and t are parallel. Line w is perpendicular to them. If the slope of line t is

 $-\frac{1}{3}$  what is the slope of line w?

•  $-\frac{1}{3}$  

•  $\frac{1}{3}$  

•  $3$  

•  $-3$  

• Not enough information to tell.

Multiple Select

Graph the following lines on desmos. Select the parallel lines.

• lines p and q only

• lines p, q and s only

• lines p, q, and r only

• all lines are parallel