Question

Learning task3:A. Change the following into the form of f(x) = mx + b

1.y-3x=7
2. 2x + 4y =8
3. -x + y =5
4.y + 5 = -2x
5. 3x + 2y - 4 = 0

Answer 1

1. f(x) = 3x + 7

2.
`f(x) = -\frac12x + 2`

3. f(x) = x + 5

4. f(x) = -2x - 5

5.
`f(x) = -\frac32 x + 2`

Explanation:

Rearrange all the equations to make y the subject,
then substitute f(x) for y:

1. y - 3x = 7

Add 3x to both sides:

⇒ y = 3x + 7

⇒ f(x) = 3x + 7

2. 2x + 4y = 8

Subtract 2x from both sides:

⇒ 4y = -2x + 8

Divide both sides by 4:

⇒
`y = -\frac12x + 2`

⇒
`f(x) = -\frac12x + 2`

3. -x + y = 5

Add x to both sides:

⇒ y = x + 5

⇒ f(x) = x + 5

4. y + 5 = -2x

Subtract 5 from both sides:

⇒ y = -2x - 5

⇒ f(x) = -2x - 5

5. 3x + 2y - 4 = 0

Subtract 3x from both sides:

⇒ 2y - 4 = -3x

Add 4 to both sides:

⇒ 2y = -3x + 4

Divide both sides by 2;

⇒
`y = -\frac32 x + 2`

⇒
`f(x) = -\frac32 x + 2`