Slope Review for Geometry

Identifying Slope of a Line

• Slope can tell us the direction of the line!

• Refresh yourself of the 4 types of slope using the picture to the right:

Multiple Choice

What type of slope?

• positive

• negative

• zero

• undefined

Multiple Choice

What type of slope?

• negative
• steep
• undefined
• zero slope

Multiple Choice

What type of slope?

• zero slope
• undefined
• negative
• positive

Multiple Choice

What type of slope?

• undefined
• positive slope
• negative slope
• zero slope

Finding the Slope of a Line

• Slope can tell us how steep a line is!

• Each line can be assigned a value (a #) that tells us how steep the line is.

• Slope is written as a ratio (rise/run)

• Always make sure to simplify your answer!

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{2}{3}$$

• $$\frac{3}{2}$$

• 3

• $$\frac{1}{3}$$

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{1}{2}$$  

• $$\frac{2}{1}$$  

• 2

• 1

Multiple Choice

Find the slope of the line below using rise/run.

• 3

• $$\frac{1}{3}$$  

• 2

• 1

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{5}{3}$$  
  

• $$\frac{3}{5}$$  
  

• 5

• $$\frac{5}{4}$$  
  

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{1}{2}$$  
  

• $$\frac{4}{2}$$  
  

• 2

• 3

• $$\frac{2}{3}$$  

Parallel Lines

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

SLOPE of Parallel Lines

In the coordinate plane,

Parallel Lines have the SAME SLOPE

Multiple Choice

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

• $$\frac{2}{3}$$  

• $$-\frac{2}{3}$$  

• $$\frac{3}{2}$$  

• $$4$$  

• $$-4$$  

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?

• $$y=-\frac{1}{4}x-25$$

• $$y=\frac{1}{4}x+2$$

• $$y=-4x-25$$

• $$y=4x+13$$

• $$y=\frac{1}{4}x+9$$

What about equations in different forms?

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

But...

What about equations in different forms?

​Are y = 2x + 4 and 2x + 5y = 10 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 Select

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

• $$y=\frac{5}{8}x-1$$  

• $$y=-\frac{5}{8}x+13$$  

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

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

• $$y-2=-\frac{5}{8}\left(x+3\right)$$  

Perpendicular Lines

Lines that intersect at a right (90 degree) angle

SLOPE of Perpendicular Lines

In the coordinate plane, Perpendicular Lines

have slopes that are OPPOSITE RECIPROCALS

Multiple Select

Which two lines are perpendicular?

• $$y=\frac{3}{7}x-25$$

• $$y=-\frac{3}{7}x+2$$

• $$y=-\frac{7}{3}x-25$$

• $$y=3x+13$$

• $$y=7x+9$$

In the coordinate plane, Perpendicular Lines

have slopes that are OPPOSITE RECIPROCALS

What about equations in different forms?

Multiple Choice

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

• $$y=-\frac{5}{6}x-2$$  

• $$y=\frac{5}{6}x+13$$  

• $$y=\frac{6}{5}x+11$$  

• $$y=-\frac{6}{5}x-100$$  

Special Opposite Reciprocal Example

​

​EXAMPLE

​What is the opposite reciprocal of 4?

Multiple Select

Which line(s) are perpendicular to the line:  $$8x+2y=22$$  

• $$y=\frac{1}{4}x-1$$  

• $$y=-\frac{1}{4}x+13$$  

• $$y-12=-\frac{1}{4}\left(x+13\right)$$  

• $$y-5=4\left(x+8\right)$$  

• $$y-2=\frac{1}{4}\left(x+3\right)$$  

Change standard form first by adding/subtracting the "x" term.

4x + 2y = 14

-4x

2y = -4x + 14

Then Divide by the coefficient of the "y" value.

2y = -4x + 14

divide by 2

y = -2x + 7

Now the equation is in slope-intercept form

y = -2x + 7

Where the slope is -2

and the y-intercept is (0, 7)

Multiple Choice

Which equation is in standard form?

• y = -2x + 7

• 2y = -4x + 14

• 4x + 2y = 14

• y-intercept is (0, 7)

Multiple Choice

What is the slope of the equation: y = -3x - 5?

• m = -3

• m = -5

• No slope given

• m = 0

Multiple Choice

What is the y-intercept of the equation: y = -3x - 5?

• (0, -3)

• (0, -5)

• (0, 0)

• Undefined

Multiple Choice

Convert the following equation from standard form to slope-intercept form: 4x + 2y = 14

• y = 4x + 14

• y = -2x + 14

• y = -2x - 14

• y = -2x + 7

Multiple Choice

Convert the following equation from standard form to slope-intercept form: -9x +3y = -12

• y = -3x - 4

• y = -3x + 4

• y = 3x + 4

• y = 3x - 4

Multiple Choice

Convert the following equation from standard form to slope-intercept form: 2x - 2y = 6

• y = 2x - 6

• y = x - 3

• y = x + 3

• y = 2x + 6

Multiple Choice

Convert the following equation from standard form to slope-intercept form: 6x - 2y = 10

• y = 3x - 5

• y = 3x + 5

• y = -3x + 5

• y = -3x - 5