10/18 Slope from graph and Equations

10/18 Slope from Equations and Graphs

by Kristine Kunkel

​Slope Intercept Form: y = mx + b

• m= slope

• ​b= y-intercept

​Example: y = 2x - 5

​m = 2

​b = -5

Multiple Choice

Identify the slope of the function.

• 6

• $$\frac{4}{5}$$

• $$-\frac{4}{5}x$$

• $$-\frac{4}{5}$$

Multiple Choice

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

• 2
• 3
• 5
• Cannot be Determined 

Multiple Choice

Identify the slope from the equation y = -8x

• m = -8

• m = 8

• m = x

• m = -8x

Multiple Choice

What is the y-intercept of the line: y = -2x + 6

• y

• unknown

• -2

• 6

Multiple Choice

What is the slope of the line: y = -3/4x +2

• -3/4

• -2

• 4

• -2

Multiple Choice

What is the y-intercept of this line: y = 5x

• 5

• 0

• -5

• Not enough information

​Standard Form: ax +by = c

Convert standard form to

slope-intercept form to identify the slope and y-intercept

​

​Example: 2x +3y = 9

​ 3y = -2x + 9

​ y = -2/3x + 3

​

​m = -2/3

​b = 3

Multiple Choice

Write in slope intercept form. 2x + y = 2

• y = -2x
• y= 2x + 2
• y= -2x + 2
• x = -2x + 2

Multiple Choice

Find the slope of the following equation. (Hint: put in slope-intercept form)
3x-6y=12

• 3
• -3
• -1/2
• 1/2

Multiple Choice

Write the equation in slope-intercept form:
-10x + 2y = 14

• y = 10x + 12
• y = 10x + 7
• y = 5x + 14
• y = 5x + 7

Multiple Choice

What is the slope of the line with the equation. (Hint: put in slope-intercept form)
 -5x + y = 11?

• -5
• 11
• 5
• -11/5

Multiple Choice

Determine the y-intercept for the following equation. (Hint: put in slope-intercept form)
4x + 2y = -12

• 4
• -6
• -12
• 2

Multiple Choice

Put the equation in slope-intercept form:
5x - y = 16

• -y = 5x + 16
• y = 5x + 16
• x = 5y - 16
• y = 5x - 16

Multiple Choice

Put the equation in slope-intercept form: 
2x + 2y = 6

• y = - x + 3
• y = x + 3
• y = 2x +6
• y = - 2x + 6

​Point-Slope Form:

​The slope is the number in front of the parenthesis. To identify the

y-intercept, convert to slope intercept form.

​

​Example: y-3 = 2(x+5)

​m = 2

​

y-3 = 2x +10

​y = 2x +13 b = 13

​

Multiple Choice

Write the following equation in slope intercept form:

y - 3 = 3(x - 1)

• y = 3x + 6

• y = 3x - 6

• y = 3x

• y=3x - 4

Multiple Choice

Write the following equation in slope intercept form:

y + 9 = 3(x - 1)

• y = 3x + 12

• y = 3x - 12

• y = 3x - 6

• y = 3x + 6

Multiple Choice

Write the following equation in slope intercept form:

y - 3 = -2(x + 4)

• y=2x-5

• y=-2x+7

• y=-2x-5

• y=-2x +1

Multiple Choice

What is the first step to convert this equation into slope-intercept form? $$y+4=-9\left(x+3\right)$$  

• Subtract 4 from both sides of the equation

• Add 4 to both sides of the equation

• Distribute -9 to everything in the parentheses

• Distribute 9 to everything in the parentheses

​Slope from a Graph

​Count from one point to another: rise over run

​The y-intercept is where the line crosses the graph

​

​

​Example pictured: m = 2/4 = 1/2

​y -intercept = 0

Multiple Choice

Find the slope:

• 3/4
• 4/3
• -3/4
• -4/3

Multiple Choice

Find the slope:

• 2
• -2
• 1/2
• -1/2

Multiple Choice

Find the slope

• -5/3
• -3/5
• 5/3
• 3/5

Multiple Choice

Find the rate of change

• 3
• -3
• -1/3
• 1/3

Multiple Choice

Find the slope of the line.

• 1/2
• -1/2
• 2
• -2

Multiple Choice

Find the slope of the line.

• 1/4
• -1/4
• -4
• 4

Multiple Choice

Find the slope of the line. 

• 0
• 1
• undefined 
• -1

Multiple Choice

Find the slope of the line. 

• undefined
• 1
• zero
• -1

Multiple Choice

Which of these lines has a slope of -3?

• A
• B
• C
• D