Notes on Proportional and Non-Proportional Equations (8th Grade Math)

Proportional Equation: y = mx

• y is always a multiple of x (they change together at the same rate).

• m is the slope (how much y increases when x increases by 1).

• The graph line goes through the origin

• y is the answer you get from the equation.

Non-Proportional Equation: y = mx + b

• y changes with x, but there is also a starting value (b) when x is 0.

• m is still the slope.

• b is the y-intercept (where the line crosses the y-axis).

• The line doesn’t go through the origin.

• Example: If y = 2x + 3, then when x = 0, y = 3.

• y is the answer you get from the equation.

Key Differences

How to Tell if a Table is Proportional:

- Pick at least two x and y value pairs from the table.

- Use the formula: y/x for each pair (make them into ratios).

- Compare the ratios.

- If the ratios are all the same, the table is proportional.

- If the ratios are different, the table is not proportional.

Key Differences

• y = mx: Proportional, passes through (0,0), no y-intercept (b).

• y = mx + b: Not always proportional, can cross the y-axis anywhere (b can be any number).