Horiz. & Vert. Lines, Parallel & Perp., Point-Slope, Word Probs

Horiz. & Vert. Lines, Parallel & Perp., Point-Slope, Word Probs

By Shalynne Orth

Vertical and Horizontal Lines

Multiple Choice

What is the equation of the line shown?

• $$x=-2$$

• $$y=-2$$

• $$x=2$$

• $$y=2x$$

Multiple Choice

What is the slope of the line shown?

• -2

• 2

• 0

• undefined

Multiple Choice

What is the equation of the line shown?

• $$x=3$$

• $$y=3$$

• 0

• undefined

Multiple Select

Which of the statements about HORIZONTAL lines are true? (check all that apply)

• their slope is 0

• the equation is x = c

• their slope is undefined

• the equation is y = c

Multiple Select

Which of the statements about VERTICAL lines are true? (check all that apply)

• their slope is 0

• the equation is x = c

• their slope is undefined

• the equation is y = c

4.6A Parallel and Perpendicular Lines

Parallel Lines

• Have the same slope

• Have different y-intercepts

• Never intersect

Multiple Choice

Parallel lines have....

• Same slope and the same y-intercept

• Different lopes and the same y-intercept

• Same slope and different y-intercepts

• Different slopes and different y-intercepts

Multiple Choice

What slope is parallel to a slope of 2?

• 1

• $$-\frac{1}{2}$$

• $$\frac{1}{2}$$

• 2

Multiple Choice

Which of the following equations is parallel to  $$y=\frac{1}{2}x+5$$  ?

• $$y=-\frac{1}{2}x-3$$  

• $$y=-2x+4$$  

• $$y=\frac{1}{2}x-3$$  

• $$y=\frac{1}{2}x+5$$  

Multiple Choice

If Jaid and Toni both made 5 dollars an hour but Jaid started with 6 dollars and Toni started with 10 dollars. Will they ever have the same amount of money?

• Yes

• No

Perpendicular Lines

• Have opposite reciprocal slopes

• Can have the same y-intercept

• Intersect at a 90 degree angle

Opposite Reciprocal

• Flip the numbers

• Flip the sign

Multiple Choice

The opposite reciprocal to $$\frac{5}{2}$$  is?

• $$\frac{2}{5}$$  

• $$-\frac{5}{2}$$  

• $$\frac{5}{2}$$  

• $$-\frac{2}{5}$$  

Multiple Choice

Which slope would be perpendicular to a slope of $$2$$  ?

• $$2$$  

• $$\frac{1}{2}$$  

• $$-\frac{1}{2}$$  

• $$-2$$  

Multiple Choice

Which equation is perpendicular to  $$y=\frac{2}{3}x-4$$ ?

• $$y=-\frac{3}{2}x+4$$  

• $$y=-\frac{2}{3}x+4$$  

• $$y=\frac{2}{3}x-4$$  

• $$y=\frac{3}{2}x-4$$  

Multiple Choice

Are the given lines parallel, perpendicular, or neither? $$y=\frac{1}{2}x+2$$  and $$y=\frac{1}{2}x-4$$  

• Parallel

• Perpendicular

• Neither

Multiple Choice

Are the given lines parallel, perpendicular, or neither? $$y=2x+3$$  and  $$y=-\frac{1}{2}x+3$$  

• Parallel

• Perpendicular

• Neither

​What is Point Slope Form?

Multiple Choice

What is point slope form?

• $$y=mx+b$$  

• $$m=\frac{y_2-y_1}{x_2-x_1}$$  

• $$y-y_1=m\left(x-x_1\right)$$  

• $$y-x=m\left(x_1-y_1\right)$$  

Multiple Choice

What is the slope of the equation y-5=7(x-3)

• 7

• 7/5

• -7

• 4

Multiple Choice

Write an equation is point-slope form for each line.

Slope is 1/3 and (-3, 1) is on the line.

• $$y+3=\frac{1}{3}\left(x-1\right)$$  

• $$y+1=\frac{1}{3}\left(x-3\right)$$  

• $$y-3=\frac{1}{3}\left(x+1\right)$$  

• $$y-1=\frac{1}{3}\left(x+3\right)$$  

Multiple Choice

Write the equation of the line

in Point-Slope form that goes through

the point (10,5) and has a slope of -3

• y - 5 = -3(x - 10)

• y= -3x + 35

• y + 5= -3(x + 10)

• y= -3x - 35

point slope form

How to write an equation of a line given 2 points

Write the equation of a line through the points (4, 0) and (-1, 10)

Multiple Choice

What is the slope of the line through the points (4, 0) and (-1, 10)?

• -10/3

• 3/10

• 2

• -2

Slope of line through (4,0) and (-1,10)

Multiple Choice

Write the equation in point-slope form for the line that contains the points
(-2, -3), (4, 3)

• y - 3 = 1(x - 2)
• y + 3 = 1(x + 2)
• y -3 = -1(x + 2)
• y + 3 = -1(x - 2)

Multiple Choice

Write the equation in point-slope form

for the line that contains the points

(3, -5) and (5, - 1)

• y - 5 = 2(x + 3)

• y + 5 = 2(x - 3)

• y - 3 = 2(x + 5)

• y + 3 = 2(x - 5)

Multiple Choice

Convert the equation of the line

y + 5 = -3(x - 6)

into slope intercept form.

(AKA Solve for Y!)

• y = -3x - 23

• y = -3x - 13

• y = -3x - 11

• y = -3x + 13

Word Problems - Linear Functions

Multiple Choice

The local service center advertises that it charges a flat fee of $50 plus $8 per mile to tow a vehicle. Write an equation that represents the total cost (C) of a service for m miles of towing.

• y = 8x + 50

• C = 50m +8

• y = 50x + 8

• C = 8m + 50

Multiple Choice

Write and solve a linear equation in slope-intercept form 

$$y=mx+b$$   where m is the rate of change and b is the starting point.

• Total cost is $1.29 per song

• Total cost is $2 for the app

• Total cost is $40.70 to download 30 songs

• Total cost is $38.70 to download 30 songs

Multiple Choice

Write and solve a linear equation in standard form

$$Ax+By=C$$

• 888 children

• 700 children

• $1.50 per adult
  

• $4,050

Multiple Choice

While on vacation in Washington DC, the cab ride for the Dulles airport to the hotel is 15 miles. The total cost of the cab ride is $25.50. The cab driver charges you $1.50 per mile for the entire trip.

What is an ordered pair given in this situation? (x,y)

• (1.50, 0)

• (1.50, 15)

• (15, 25.50)

• (25.50, 15)

Multiple Choice

While on vacation in Washington DC, the cab ride for the Dulles airport to the hotel is 15 miles. The total cost of the cab ride is $25.50. The cab driver charges you $1.50 per mile for the entire trip.

Write an equation that can be used to determine the cost of a cab ride.

• $$y-25.50=1.50\left(x-15\right)$$

• $$y-15=1.50\left(x-25.50\right)$$

• $$y+15=1.50\left(x+25.50\right)$$

• $$y+25.50=1.50\left(x+15\right)$$