Linear Relationships Prep

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It shows a constant rate of change.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant value (k) that relates two proportional quantities. It is found by dividing one quantity by the other.

Front

If 14 gallons of gas cost $48.86, what is the cost per gallon?

Back

$3.49 per gallon.

Front

How do you find the slope of a linear relationship?

Back

The slope (m) is found by taking the change in the y-values divided by the change in the x-values (m = Δy/Δx).

Front

What does the y-intercept represent 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

What is the formula for a linear equation in slope-intercept form?

Back

The formula is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship where two quantities maintain a constant ratio or rate.

Front

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

Back

If the ratios of corresponding values are constant, the relationship is proportional.

Front

What is the difference between direct variation and inverse variation?

Back

Direct variation means as one variable increases, the other increases (y = kx). Inverse variation means as one variable increases, the other decreases (y = k/x).

Front

What is the significance of the slope in a real-world context?

Back

The slope represents the rate of change, such as speed, cost per item, or growth rate.