Each line represents a proportional relationship. Write an equation for each line. Show your work.

The equation of line a is y = x

The equation of line b is y =   x

Step-by-step explanation:

The equation of the proportional is y = m x, where

The rule of the slope of a line is m = , where

∵ Line a passes through points (0, 0) and (3, 3)

∴ x1 = 0 and y1 = 0

∴ x2 = 3 and y2 = 3

→ Substitute them in the rule of the slope above

∵ m =

∴ m = 1

→ Substitute in the form of the equation above

∴ y = (1)x

∴ y = x

∴ The equation of line a is y = x

∵ Line b passes through points (0, 0) and (3, 2)

∴ x1 = 0 and y1 = 0

∴ x2 = 3 and y2 = 2

→ Substitute them in the rule of the slope above

∵ m =

∴ m =

→ Substitute in the form of the equation above

∴ y = () x

∴ y =   x

∴ The equation of line b is y =   x

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.