Review of Slopes

Review of SLOPE
parallel & perpendicular lines

Multiple Choice

Rewrite this equation in slope intercept form (y = mx + b):

9x + 3y = -6

• 3y = 9x -6

• y = -3x -2

• y = -9x - 6

• y = -3x +2

Multiple Choice

Rewrite this equation in slope intercept form (y = mx + b):

6x - 2y = 10

• 2y = 6x - 10

• y = -3x - 5

• y = 3x - 5

• y = -3x + 5

Multiple Choice

What is the slope in the equation y=2x + 3?

• 2

• 3

• 5

• Cannot be Determined 

Multiple Choice

Write a linear equation in slope intercept form of a line with a slope of 12 and y intercept of 10

• y=12x-10

• y=10x+12

• y=12x+10

• x=10x-12

slope is the rate of change

​slope = "rise over run"
slope = vertical change divided by horizontal change
m=(y₂-y₁)/(x₂-x₁)​

​Remember Slope?

Multiple Choice

Find the slope

• -5/3

• -3/5

• 5/3

• 3/5

1. Identify the coordinates for 2 points on the line

2. Count the vertical distance (up+ or down-) from first point to second

3. Count horizontal "blocks" (left- or right+) from first point to second

4. Write the slope as the ratio of vertical/horizontal

​

HOW TO Find slope from a graph:

Multiple Choice

Find the slope of the line.

• -2

• 2

• -1

• 1

Multiple Choice

Find the slope:

• 3/4

• 4/3

• -3/4

• -4/3

1. Identify one point as (x₁, y₁) and the second as (x₂, y₂)

2. Find the vertical distance (y₂-y₁)

3. Find the horizontal distance (x₂-x₁)

4. Write the ratio of vertical/horizontal distances (you might have to reduce)

​

​Find the slope of the line thru 2 points:

Multiple Choice

Find the slope of the line that passes through:
(6,7) and (4,2)

• 2/5

• -5/2

• 5/2

• -1/2

Multiple Choice

Find the slope of the line that passes through: 
(2, 4) and (6, 12)

• 1/2

• -1/2

• 2

• -2

Multiple Choice

Find the slope of the line that passes through:
(10, 1) and (5, 2)

• 1/5

• -1/5

• 5

• -5

Multiple Choice

Find the slope:

• 2

• -2

• 1/2

• -1/2

HORIZONTAL LINES--vertical change =0
0/#=0

VERTICAL LINES--horizontal change =0
#/0=UNDEFINED

​

Types of Slopes

Multiple Select

Which of the following have UNDEFINED SLOPES? (Select ALL that Apply)

• y=3

• x=3

Multiple Choice

What kind of slope does the graph have?

• Positive

• Negative

• 0

• Undefined

Parallel lines lie in the same plane and never intersect.
What do you notice when you compare the slopes of two parallel lines?

​

Parallel Lines

Multiple Choice

Slopes of parallel lines are...

• opposite reciprocals.

• opposites.

• identical.

• always 7.

​Remember PERPENDICULAR Lines intersect to FORM RIGHT ANGLES

Slopes are OPPOSITE SIGNS and "FLIPPED"

​

Perpendicular Lines

Multiple Choice

y = 3x +2
y = 3x - 3
These lines are...

• Parallel

• Perpendicular

• Neither

• The same line

Multiple Choice

Slopes of perpendicular lines are...

• opposite reciprocals.

• opposites.

• identical.

• always 7.

Multiple Choice

What slope is parallel to:  
m = 3/4

• 4/3

• 3/4

• -3/4

• -4/3

Multiple Choice

What slope is perpendicular to:  
m = 5/8

• -5/8

• 5/8

• -8/5

• 8/5

Multiple Choice

What slope is parallel to:  
m = 4

• 4

• -1/4

• -4

• 1/4

Multiple Choice

y = 5/7x +2

y = 5/7x - 30

These lines are...

• Parallel

• Perpendicular

• Intersect

Multiple Choice

y = 6x + 2

y = -6x + 2

These lines are...

• Parallel

• Perpendicular

• Intersecting (neither parallel nor perpendicular)

Be careful!
Lines that do not meet BOTH opposite signs AND reciprocals are merely Intersecting (But NOT perpendicular)

Multiple Choice

Are these two lines parallel, perpendicular or neither?
y = -1/3x - 5
y = 1/3x + 2

• Parallel

• Perpendicular

• Neither

Multiple Choice

Are these two lines parallel, perpendicular or neither?

y = -1/4 x - 5

y = 4x + 2

• Parallel

• Perpendicular

• Neither

Multiple Choice

Find the slope PARALLEL to a line that passes through the points (4, 2)
and (– 8, 5)

• $$m_{\parallel}=\frac{4}{3}$$

• $$m_{\parallel}=-\frac{3}{12}$$

• $$m_{\parallel}=\frac{3}{12}$$

• $$m_{\parallel}=-\frac{12}{3}$$

Multiple Choice

Find the slope PERPENDICULAR to a line that passes through the points (4, 2)
and (– 8, 5)

• $$m_{\perp}=\frac{12}{3}$$

• $$m_{\perp}​=-\frac{12}{3}$$

• $$m_{\perp}=\frac{3}{12}$$

• $$m_{\perp}=-\frac{3}{12}$$