m8 chapter 4 extra credit

Finding the Slope

• Count up or down from to the other

• Count left or right from one point to the other

• Down is negative movement, up is positive movement

• Left is negative movement, right is positive movement

How to find the slope:

• 1. choose two points on the line

• 2. find the change in y-values (rise). if you move up the change is positive & if you move down the change is negative

• 3. find the change in x-values (run). if you move right the change is positive & if you move left the change is negative

• 4. slope = rise / run

Sometimes slopes will be undefined or have a slope of zero.

When a slope is in a completely straight horizontal line, then the slope is considered zero.

When a slope is in a completely straight vertical line, then the slope is considered undefined.

The slope of this line is zero

The slope of this line is undefined

Remember, a slope is positive when the staircase is going up.

The image to your right shows a positive slope.

Remember, a slope is negative when the staircase is upside down.

The image to your right shows a negative slope.

Don't forget that your slopes should be simplified.

If you have a slope of 10/5, it can be simplified to 2/1

Multiple Choice

Slope is know as rise/

• run
• fall
• none
• rise

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Find the slope of the line.

• 1/4

• -1/4

• -4

• 4

Multiple Choice

Find the slope of the line.

• 1/2
• -1/2
• 2/1
• -2/1

Multiple Choice

Find the slope of the line.

• Undefined
• 0
• 1
• -1

Multiple Choice

Find the slope

• 5/2
• -5/2
• 2/5
• -2/5

Multiple Choice

Find the slope

• -3/4
• 4/3
• 3/4
• -4/3

Multiple Choice

Which slope is positive?

Multiple Choice

Which slope is zero?

Multiple Choice

Which slope is negative?

Multiple Choice

Which slope is undefined?

Multiple Choice

Find the slope:

• 3/4
• 4/3
• -3/4
• -4/3

Slope Formula

How can we use the slope formula to find the slope of two given points?

You can use any two points on a line to find the slope

.

Lets Practice!

Step by Step

• 1. Label the points

• (It doesn't matter which point you pick to be first or second you'll still get the same answer)

Lets Practice!

Step by Step

• 2. Substitute or plug in the numbers into the slope formula

• 3. Use the formula to calculate the slope and simplify

Multiple Choice

What is the slope formula?

Multiple Choice

Find the slope of the line that goes through the points

(−1,−2) and (−3,−4).

• 1

• 2

• 3

• 4

Multiple Choice

Find the slope of the line that goes through the points

(−11,−5) and (1,−12)

• $$-\frac{5}{8}$$

• $$\frac{16}{11}$$

• $$\frac{1}{6}$$

• $$-\frac{7}{12}$$

Multiple Choice

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

• 1/5

• -1/5

• 5

• -5

Multiple Select

Which of the following is the correct write the slope formula for the points (2, 4) and (6, 12)? Select all that apply.

• $$\frac{2-4}{6-12}$$  

• $$\frac{12-4}{6-2}$$  

• $$\frac{4-12}{6-2}$$  

• $$\frac{4-12}{2-6}$$  

Multiple Choice

Gus wants to find the slope of a line that passes through the points (3,9) and (8,2) but they made a mistake in their work: $$m=\ \frac{9-2}{8-3}$$  .

What is the correct way to write out the formula ?

• $$\frac{2-9}{3-8}$$  

• $$\frac{3\ -8}{9-2}$$  

• $$\frac{2-9}{8-3}$$  

Multiple Choice

• 1/6

• 1

• -1/6

• -1

Multiple Choice

• 1/-2

• 5/14

• 1/2

• -1/2

Match

Match the following

-1/3

0

undefined

-2

-3/2

• -1/3

• 0

• undefined

• -2

• -3/2

Match

Match the following

-1

0

-7/2

undefined

• -1

• 0

• -7/2

• undefined

"Slope intercept form" of a line is a convenient way to identify the slope and y - intercept (the point where the line and y axis intersect)

Multiple Choice

Which equation is slope intercept form?

• y = mx + b

• $$\frac{y_2-y_1}{x_2-x_1}$$  

• ax + by = c

• $$A\ =\ \pi r^2$$  

Multiple Choice

Which equation is in slope intercept form?

• y - 3 = x + 3

• y = 3x - 1

• y = 3x -6 y

• $$y\ =\ \frac{4}{x}$$  

Multiple Choice

Which equation is in slope intercept form?

• $$y\ =\ y$$  

• $$y\ +\ x\ =\ 12$$  

• $$y\ =\ \frac{1}{2}x$$  

• $$y\ =\ x^2$$  

Multiple Choice

What does 'b" represent in y=mx+b

• y-intercept
• beans
• x-intercept
• slope

Multiple Choice

What does "m" represent in y=mx+b?

• y-intercept
• slope
• macaroni
• x-intercept

Multiple Choice

What is the slope in the equation:  y=4x+3

• 3
• 4x
• 4
• 3x

Multiple Choice

What is the y-intercept in the following equation:  y=-4x-5

• -4
• 4
• 5
• -5

​Visual:

Identifying m & b in equations (y=mx+b)

• y= 4x - 3 ..... m= 4 , b= -3

• y = -3x + 7 ..... m= -3 , b= 7

• y = x - 8 ..... m= 1 , b= -8

• y = -x ..... m= -1 , b= 0

• y = 5x + 10 ..... m= 5 , b= 10

Multiple Choice

y = -7x +9

Identify the slope

• m= 9

• m=-7

• m= 7x

• m= -7x

Multiple Choice

y = -7x +9

Identify the y-intercept

• b= 9

• b=-7

• b= 7x

• b= -7x

Multiple Choice

y = -x -10

Identify the m & b

• m= -x , b= -10

• m= -x , b= 10

• m= -1 , b= -10

• m= -1 , b= 10

Multiple Select

Given:  $$y=-\frac{1}{3}x+5$$ , find the slope and y-intercept.

• Slope:  $$-\frac{1}{3}$$  

• y-intercept:  $$5$$  

• Slope:  $$5$$  

• y-intercept:  $$-\frac{1}{3}$$  

• Slope:  $$-\frac{1}{5}$$  

Multiple Select

Given:  $$y=-5x+3$$ , find the slope and y-intercept.

• Slope:  $$-5$$  

• y-intercept:  $$3$$  

• Slope:  $$5$$  

• y-intercept:  $$-3$$  

• Slope:  $$-\frac{1}{5}$$  

Multiple Select

Given:  $$y=\frac{3}{5}x$$ , find the slope and y-intercept.

• Slope:  $$\frac{3}{5}$$  

• y-intercept:  $$0$$  

• Slope:  $$1$$  

• y-intercept:  $$1$$  

• y-intercept:  $$\frac{3}{5}$$  

Multiple Select

Given:  $$y=4$$ , find the slope and y-intercept.

• Slope:  $$0$$  

• y-intercept:  $$4$$  

• Slope:  $$4$$  

• y-intercept:  $$0$$  

• Slope:  $$1$$  

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

Which graph represents the function:   $$y=x+3$$  

Multiple Choice

Write the equation when given the slope (m) = -1 and y-int. (b) =2 .

• y= x + 2

• y= -x + 2

• y= -2 + x

Multiple Choice

Write the equation when given the slope (m) = 1/2 and y-int. (b) = 3/2 .

• y= 3/2 + 1/2x

• y= -1/2x - 3/2

Multiple Choice

Write the equation when given the slope (m) = 0 and y-int. (b) = -4 .

• y= -4

• y= -4x

Slope-intercept Form

• y = mx + b

• m represents the slope, rate of change, rise/run

• b represents the y-intercept, place the graph touches the y-axis

• Example: y=3x+4

• m(slope)=3

• b(y-intercept)=4

Graphing

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

Graphing

Graph $$y=-\frac{4}{5}x+4$$

Graphing

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

Graphing

Graph $$y=-x+3$$

Graphing

Graph $$y=-\frac{5}{3}x+5$$

Graphing

Graph $$y=3x$$

Graphing

Graph $$y=\ -2x+2$$

Graphing

Graph $$y=\frac{2}{5}x-7$$

Graphing

Graph $$y=\frac{-7}{8}x$$

Graphing

Graph $$y=\frac{3}{2}x+1$$

Graphing

Graph $$y=-4x-4$$