Linear Equations Integer Solutions

Weeks 1-3 Consolidation

Lesson 1 - Integer Operations

We learnt:

• To know the numbers in the set of integers

• To know the rules for the mathematical operations applied to negative numbers

• To understand the notation for powers and roots

• To be able to evaluate operations on integers including negative numbers, powers and roots and apply order of operations

Reorder

Reorder the following

• -10

• -5

• 0

• 5

• 10

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Lesson 2 - Linear Equations

We learnt:

• To be able to solve a linear equation by using inverse operations

• To know that an answer can be checked by substituting into the original equation

• To know that equations involving brackets can be solved by first expanding the brackets

• To know to solve equations with variables on both sides by collecting variables on one side of the equations

Math Response

Solve for x:

$$2x\ +\ 3\ =\ 4$$

Type answer here

Correct Answer: \frac{1}{2}

Deg^°

Rad

Math Response

Solve for x:

$$\frac{x}{4}-3=7$$

Type answer here

Correct Answer: 40

Deg^°

Rad

Math Response

Solve for x:

$$2\left(3x-4\right)\ =\ 11$$

Type answer here

Correct Answer: \frac{19}{6}

Deg^°

Rad

Math Response

Solve for x:

$$5x-2\ =\ 3x-4$$

Hint: have all the x's on one side

Type answer here

Correct Answer: -1

Deg^°

Rad

Lesson 3 - Linear Equations

We repeated this lesson...

You may like to revisit this soon to refresh your mind if you struggled with the four questions!

Lesson 4 - Intro to Linear Relations

We learnt:

• Review features of the Cartesian plane and coordinate pairs

• Review plotting graphs of linear relations using a table of values

Time to grab your Cartesian Planes!

Draw

Create a table of values for the following equation

$$y\ =\ x+2$$

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Poll

Decide if the point (-2, 4) is on the line $$y\ =\ 2x\ +10$$

• Yes

• No

Draw

Decide if the point (-2, 4) is on the line $$y\ =\ -x+2$$

Lesson 5 - Midpoint and Line Segments

Graphing

Plot the points (3, 0) and (5, 2), then plot the midpoint.

Multiple Choice

Find the length of the segment by joining the points and correct to 2 decimal places.

(1, 1) and (2, 6)

Hint: use the cartesian plane and draw

Another hint: use $$a^2+b^2=c^2$$

• 4.10

• 5.10

• 6.10

• 7.10

Lesson 6 - Gradient

We learnt how to:

• Identify the gradient of a line as either negative, positive, zero or undefined

• Calculate gradient using rise and run
  
  Don't put those Cartesian Planes away!

Draw

Draw a line with a positive gradient in RED, negative gradient in YELLOW, and a zero gradient in BLUE

Match

Match the following graphs to their gradient answer

m = 2

m = -3/2

m = 3/5

• m = 2

• m = -3/2

• m = 3/5

Match

Match the following points to their gradient

• (2, 3) and (3, 5)

• (2, 1) and (5, 5)

• (1, 5) and (2, 7)

• (-2, 6) and (0,8)

m = 2

m = 4/3

m = 2

m = 1

• m = 2

• m = 4/3

• m = 2

• m = 1

^{Lesson 7 - More Gradients and Lines with Intercepts}

• Recall the linear equation y=mx+c and its important parts 

  • m is the gradient 

  • c is the y-intercept 

• Use the gradient formula 

• Rearrange formulae to match the linear equation format 

• Substitute points into equations to find a rule

Draw

Rearrange the following to get it into the form y=mx+c

4x + 2y = 10

Draw

Rearrange the following to get it into the form y=mx+c

6x + 2y = 4

Draw

Rearrange the following to get it into the form y=mx+c

-3x + 3y = 6

Drag and Drop

Sub the point (3, 4) into y = x + c to find the equation



y = ​

Placeholder

​

Drag these tiles and drop them in the correct blank above

x + 7

3x + 4

3 = 4 + c

Multiple Choice

Find the equation of the line for which $$m\ =\ 3,\ point\ \left(1,\ 8\right)$$

• y = 3x + 5

• 8 = 3 + 5

• y = 5x + 3

• No idea

Multiple Choice

Find the equation of the line for which $$m\ =\ -2,\ point\ \left(2,\ -5\right)$$

• y = 2x - 1

• y = -2x - 1

• y = -5x -5

• No idea