Slopes Boot Camp Day 1

Slope,
Y-Intercept,
Plotting Points

Multiple Select

What is slope? 

Hint: Pick 2 answers.

• Constant rate of change

• How the line looks

• Rise over run

Review of Graphing

Objective: Identify and graph points in the coordinate plane.

Hotspot

Which line is the X-AXIS?

Coordinate Plane

Labelling

Label each quadrant and each axis.

Drag labels to their correct position on the image

x-axis

Quadrant 2

y-axis

Quadrant 4

Quadrant 3

Quadrant 1

Graphing a Point

Always written in the form (x,y)

​

The x-value tells us to

move left or right

​

The y-value tells us to

move up or down

​

Graph (4,6)​

​

Graphing

Graph the following points: (7, -3), (-4, 5), and (8, 6)

Drag and Drop

The coordinates of point P are ​

Placeholder

, point N are ​

Placeholder

, S are ​

Placeholder

and M are ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

(2,-3)

(6,0)

(-9,0)

(7,-9)

(-3,2)

(0,6)

(-9,7)

(0,-9)

Categorize

Options (10)

(4,7)

(5,6)

(-3,8)

(-5,6)

(-6,5)

(-4,-7)

(-5,-6)

(-6,-5)

(5,-6)

(2,-9)

Organize these point to the quadrant they would be graphed into.

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

Identifying Basic Slopes

Slope: the 'steepness' of a line.

​

There are FOUR basic categories for SLOPES

POSITIVE SLOPE

NEGATIVE SLOPE

SLOPE OF ZERO

UNDEFINED SLOPE

Match

Match the following graph with its slope.

Positive Slope

Negative Slope

Slope of Zero

Undefined Slope

• Positive Slope

• Negative Slope

• Slope of Zero

• Undefined Slope

Slope

Learning Targets​

​Slope

​I can understand​ the connections between proportional relationships, lines, and linear equations. ​

​

** Are linear lines always proportional?

**Are proportional lines always linear?​

​Constant Rate of change and Steepnness of a line

​​Rate of change=y/x ​

​

The graph shows a change of $94 every 2 weeks, therefore the constant slope is $47 per week.​

What is the slope?

What is the y-intercept?

What is the equation of this line?​

​What is the slope?

What is the y-intercept?

What is the equation of this line?​

​Equations and graph of a line

​To write an equation for a line, choose two points and find the slope. Then find the y-intercept. Replace these numbers in slope-intercept form. ​

Slope= Vertical change​

Horizontal change​

Fill in the Blanks

Multiple Choice

What is the slope of the line?

• $$\frac{1}{2}$$

• 2

• -2

• $$-\frac{1}{2}$$

Multiple Choice

What is the slope of the line?

• -3

• -1

• 1

• 2

Identifying the Intercepts

​What is the x-intercept?

​

​

What is the y-intercept?​

​

Multiple Choice

What is the slope of the line?

• $$\frac{1}{2}$$

• $$2$$

• $$-\frac{1}{2}$$

• -2

Drag and Drop

The line graphed has an x-intercept of ​

Placeholder

and a y-intercept of ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

(1,0)

(0,-4)

(-4,0)

(0,1)

(1,-4)

(-4,1)

Multiple Choice

Find the slope of the line.

• 4/2

• -4/2

• 2/1

• -2/1

Multiple Choice

Find the slope of the line.

• -2/1

• 2/1

• -1/2

• 1/2

Multiple Choice

Find the slope of the line.

• 1/4

• -1/4

• -4/1

• 4/1

Multiple Choice

Find the slope of the line.

• 1/2

• -1/2

• 2/1

• -2/1

Finding the Slope Given Two Points

What if instead of having a graph, I ONLY knew the two points.

Finding the Slope Given Two Points

EXAMPLE:

Find the slope of the line that passes through (-3,7) and (0,3).​​

Multiple Choice

Which is the proper way to set up finding the slope of a line that passes through (1,-6) and (9,-8)?

• $$\frac{-6-\left(-8\right)}{1-9}$$  

• $$\frac{-6-8}{1-9}$$

• $$\frac{1-\left(-6\right)}{9-\left(-8\right)}$$

• $$\frac{-8-9}{-6-1}$$

Math Response

Find the slope of a line that passes through the given points:
(2,-2) and (5,7)

Type answer here

Correct Answer: \frac{3}{1}

Deg^°

Rad

Remember there are 2 ways to find slope

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:

(-2, 8) and (0, 8)

• 0

• -2

• 2

• 1/2

Multiple Choice

Find the slope of the line that passes through:

(-12, -5) and (0, -8)

• 1/4

• -1/4

• 4

• -4

Multiple Choice

Find the slope of the line that passes through:

(-4, 7) and (-6, -4)

• 2/11

• 13/2

• 3/10

• 11/2

Multiple Choice

Find the slope of the line that passes through:

(5, -10) and (5, -4)

• undefined

• 0

• - 14/10

• 10/14

Equations and slope of a line

​Slope-intercept form

​Slope=m

​The slope (m) of the line is the number multiplied by x to show the constant rate of change. ​

m=1/2

​How could we put this in Slope-Intercept form?

​An equation is written in slope-intercept​ form when it is solved for "y". ​

​y=mx+b

y=97x+144

Draw

What is the slope for y=56x+39?

Multiple Choice

What is the slope for y = -11/7x - 7?

• -11/7

• 11/7

• -11

• -7

Slope-intercept Form

• y = mx + b

• m represents the slope

• b represents the y-intercept

• Example: y=3x+4

• m(slope)=3

• b(y-intercept)=4

Multiple Choice

What is the slope of y=4x-6

• -6

• 6

• 4

• -4

Multiple Choice

What is the y-intercept of y=1/2x+4

• 4

• 2

• 1/2

• -4

Multiple Choice

What is the correct m and b of the equation:

$$y=-\frac{7}{2}x-3$$  

• m= $$\frac{7}{2}$$    b=3

• m= $$-\frac{7}{2}$$   b=3

• m=  $$-\frac{7}{2}$$   b=-3

• m= -3  b= $$-\frac{7}{2}$$  

Slope and Y-intercept

Table

Slope

Slope Example

Multiple Choice

What is the slope given the points (15, 8) and (10, 7)?

• 5

• $$-\frac{1}{5}$$

• $$\frac{1}{5}$$

• -5

Multiple Choice

What is the slope given the points (-2,-1) and (4,3)

• $$\frac{3}{2}$$

• $$\frac{4}{3}$$

• $$-\frac{2}{3}$$

• $$\frac{2}{3}$$

Multiple Choice

What is the slope of the table?

• 3

• -3

• $$\frac{1}{3}$$  

• $$-\frac{1}{3}$$  

Y-intercept

Table/ Two Points

Y-intercept from two points

Multiple Choice

What is the y-intercept given these two points: (3, 7) and (5, 11)

• -1

• 1

• 3

• -3

Multiple Choice

Is the point (3, 0) an x-intercept, a y-intercept, both, or neither?

• x-intercept

• y-intercept

• both

• neither

Multiple Choice

Is the point (0, -5) an x-intercept, a y-intercept, both or neither?

• x-intercept

• y-intercept

• both

• neither

Multiple Choice

Is the point (5, 5) an x-intercept, a y-intercept, both or neither?

• x-intercept

• y-intercept

• both

• neither

Fill in the Blanks

Fill in the Blanks

Multiple Choice

Identify the x-intercept of this graph.

• (-2,0)

• (-3,0)

• (0,3)

• (2,0)

Multiple Choice

What is the y-intercept of this graph.

• (0,-4)

• (-4,0)

• (0,-2)

• (0,0)

Multiple Choice

Identify the x-intercept of this graph.

• None

• (4,0)

• (0,4)

• Undefined

Multiple Choice

Does this graph have an x-intercept?

• Yes

• No

• It is not possible to determine from the graph.

Multiple Choice

Identify the x and y intercepts of this graph.

• They are both (0,0).

• They cannot be determined from the graph.

• x-intercept is (0,0).

  y-intercept is (0,-1)

• None of the above

Multiple Choice

Identify the x and y intercepts of the line graphed in the picture.

• x-intercept: Undefined

  y-intercept: 0

• x-intercept: (0,-2.8)

  y-intercept: (-3.5,0)

• x-intercept: (-3.5,0)

  y-intercept: (0,-2.8)

• x-intercept: (3.5,0)

  y-intercept: (0,2.8)