Unit 6: Linear Relationships

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 can be described by an equation of the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

What is the constant of proportionality in a linear equation?

Back

The constant of proportionality is the coefficient of x in the equation y = kx, where k is the constant. It represents the unit rate of change between the two variables.

Front

How do you find the unit rate from a given quantity?

Back

To find the unit rate, divide the total quantity by the number of units. For example, if there are 624 calories in 3 servings, the unit rate is 624 ÷ 3 = 208 calories per serving.

Front

What is the equation of a line with a slope of 5 and a y-intercept of 0?

Back

The equation of the line is y = 5x.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

What does an undefined slope mean?

Back

An undefined slope means that the line is vertical, indicating that there is no change in the x-value while the y-value changes.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The formula to calculate the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept in the equation y = 14x?

Back

The y-intercept is 0, as there is no constant term added to the equation.