Proportional/Nonproportional Equations

Front

What is a proportional relationship?

Back

A proportional relationship is one in which two quantities maintain a constant ratio. This means that as one quantity increases or decreases, the other does so in a consistent manner.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities is not constant. This often includes a fixed cost or starting point that affects the overall relationship.

Front

How do you find the slope of a linear equation in the form y = mx + b?

Back

The slope (m) is the coefficient of x in the equation. It represents the rate of change of y with respect to x.

Front

What does the slope of 2 in the equation y = 2x + 3 indicate?

Back

It indicates that for every 1 unit increase in x, y increases by 2 units.

Front

What is the equation of a proportional relationship?

Back

The equation of a proportional relationship can be expressed in the form y = kx, where k is the constant of proportionality.

Front

Identify the constant of proportionality in the equation y = 6x.

Back

The constant of proportionality is 6.

Front

What is the total cost for 10 shirts if the setup cost is $40 and each shirt costs $12?

Back

The total cost is $160, calculated as $40 + (10 shirts * $12/shirt).

Front

Which of the following equations is proportional: y = 3x + 2 or y = 6x?

Back

y = 6x is proportional because it can be expressed in the form y = kx.

Front

What is the significance of a y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

How can you tell if a relationship is proportional from a table of values?

Back

If the ratio of y to x is constant for all pairs of values, the relationship is proportional.