Unit 2 Review Lesson

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

• $$\frac{5}{4}$$  
  

Finding slope from a Table

• Slope = change in y/change in x

• Use the table to find the value the y is changing by. That is the numerator!

• Use the table to find the value the x is changing by. That is the denominator!

• ANOTHER OPTION: Graph the points and count rise/run

Multiple Choice

Find the slope. Simplify, if you can.

• $$\frac{2}{5}$$

• $$\frac{5}{2}$$

• $$2\ \frac{1}{2}$$

• 2

Multiple Choice

Find the slope. Simplify, if you can.

• $$\frac{1}{2}$$  
  

• $$\frac{4}{8}$$  

• 4

• 2

Multiple Choice

Find the slope. Simplify, if you can.

• 3

•   $$\frac{1}{3}$$  

• $$-\frac{1}{3}$$  

• -3

Slope from an equation

• The number in front of the x in the equation is the slope!

Multiple Choice

Identify the slope in the equation:

$$y=8x$$  

• 8

• 1/8

• -8

• 0

Multiple Choice

Identify the slope in the equation:

$$y=\frac{5}{6}x$$  

• $$\frac{5}{6}$$  

• $$\frac{6}{5}$$  
  

• 5

• 6

Fill in the Blanks

$y=x+5$  

Identify the slope in the equation:

​Slope Intercept Form

​y = mx + b

​slope

​y - intercept

Drag and Drop

Given:  $$y=-\frac{1}{3}x+5$$ , the slope is ​

Placeholder

and the y-intercept is ​

Placeholder

Drag these tiles and drop them in the correct blank above

5

-5

Drag and Drop

Given:  $$y=\frac{3}{5}x$$ , the slope is ​

Placeholder

and the y-intercept is ​

Placeholder

Drag these tiles and drop them in the correct blank above

0

1

Drag and Drop

Given:  $$y=4$$ , the slope is ​

Placeholder

and the y-intercept is​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

Multiple Choice

Which graph represents the function:   $$y=-\frac{1}{2}x-2$$  

Multiple Choice

Which graph represents the function:   $$y=\frac{3}{2}x+3$$  

Multiple Choice

What equation is graphed?

• $$y=5x+1$$

• $$y=-5x+1$$

• $$y=\frac{1}{5}x+1$$

• $$y=-\frac{1}{5}x+1$$

Point Slope Form

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

Multiple Choice

Write the equation in point-slope form

of the line that passes through the point

(4, -7) and has a slope of -1/4.

• y + 7 = -1/4(x - 4)

• y - 4 = -1/4(x + 7)

• y + 7 = 4(x - 4)

• y - 7 = -1/4(x - 4)

Multiple Choice

The line with the equation

y + 1 = -3(x - 5),

contains the point (5, -1)

and has a slope of _______.

• -1

• 1

• -3

• 5

Multiple Choice

For the equation
y - 3 = 2(x + 4),
which of the following is true?

• The line has m = 2 passing through the point (4, -3)
• The line has m = 2 passing through the point (3, -4)
• The line has m = 2 passing through the point (-4, 3)
• The line has m = 2 passing through the point (-3, 4)

Multiple Select

WARMUP: What is the x-intercept and the y-intercept of the line shown?

• y-intercept

  (0,-4)

• y-intercept

  (-4,0)

• x-intercept

  (0,1)

• x-intercept

  (1,0)

​EQUATIONS (functions)

​Slope-Intercept Form

y = mx + b

​STANDARD FORM

Ax + By = C

1. ​A, B and C are all integers

2. A is positive

3. The GCF of A, B and C is 1​

​Graphing in Standard Form

​Graph: 2x - 3y = 12

​x-intercept (x,0)

​y-intercept (0,y)

Drag and Drop

Given 3x + 8y = 24, the x-intercept is

Placeholder

and the y-intercept is ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

(8,0)

(0,8)

(3,0)

(0,3)

(0,6)

(6,0)

(4,0)

(0,4)

Drag and Drop

Given 2x - 8y = 48, the x-intercept is ​

Placeholder

and the y-intercept is ​

Placeholder

Drag these tiles and drop them in the correct blank above

(24,0)

(0,-6)

(0,24)

(-6,0)

(2,-8)

(-8,2)

(2,0)

(0,-8)

(0,2)

(-8,0)

To change from Standard Form to Slope Intercept Form, you solve the equation for y.

• First, add or subtract the "x" term.

• Second, divide by the coefficient (number in front of) y.

• Finally, simplify if you can.

Write 3x + 2y = 6 in slope intercept form

Multiple Choice

What is the first thing you would do to write 2x - y = 7 in slope intercept form?

• Add y to both sides

• Subtract 2x from both sides

• Divide both sides by 2

• Subtract 7 from both sides

You would subtract the 2x first

So, -y = -2x + 7 (Don't forget the negative in front of the y needs to come with it!)

Next, you would need to divide by the negative 1.

Multiple Choice

What is the resulting equation? (Remember you had -y = -2x + 7)

• y = 2x + 7

• y = -2x - 7

• y = 2x - 7

• y = 2x + 8

Multiple Choice

Which equation represents 4x - 2y = 6 in slope intercept form.

• y = 2x - 3

• y = -2x + 3

• 
  

  $$y\ =\ \frac{1}{2}x\ -\ 3$$

• y = 2x + 8

What would happen with x + 3y = -9

Multiple Choice

Write x + 5y = 10 in slope intercept form.

• $$y=-5x\ +\ 2$$

• $$y\ =\ -\frac{1}{5}x\ +\ 5$$

• $$y\ =\ 5x\ +\ 2$$

• $$y\ =\ -\frac{1}{5}x\ +\ 2$$

Multiple Choice

Write x + y = 3 in slope intercept form.

• y = x + 3

• y = -3x

• y = -x + 3

• y = -x - 3

Let's try:                 - 3x + 2y = 8

Multiple Choice

Which represents  -2x - 3y = 12 in slope intercept form.

• $$y\ =\ -\frac{2}{3}x\ -\ 4$$

• $$y\ =\ \frac{2}{3}x\ -\ 4$$

• $$y\ =\ -\frac{2}{3}x\ +\ 4$$

• $$y\ =\ \frac{2}{3}x\ +\ 4$$

Multiple Choice

Last one, which represents -x - y = 0 in slope intercept form?

• y = x

• y = -x

• y = 0

• y = x + 1