4/9 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 expressed in the form of an equation, typically y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

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

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you identify a linear equation from a set of options?

Back

A linear equation can be identified by its form, which is typically y = mx + b. Look for equations that can be rearranged into this form.

Front

What is the equation for the total cost of a service with a fixed fee and a variable cost per unit?

Back

The equation is c = vf + F, where c is the total cost, v is the variable cost per unit, f is the number of units, and F is the fixed fee.

Front

If the installation fee is $150 and the tile costs $2.75 per square foot, what is the equation for the total cost?

Back

c = 2.75f + 150, where c is the total cost and f is the area in square feet.

Front

What does it mean if an equation does not represent a real-world relationship?

Back

It means that the equation does not accurately reflect the relationship between the variables in a practical context, such as having unrealistic values or interpretations.

Front

How can you determine if a table represents a linear relationship?

Back

A table represents a linear relationship if the differences between consecutive y-values are constant for equal differences in x-values.

Front

What is the significance of the equation y = 0.5x + 7?

Back

This equation represents a linear relationship where the slope is 0.5, indicating a gradual increase in y as x increases, and the y-intercept is 7.

Front

What does the equation y = 3x represent?

Back

This equation represents a linear relationship with a slope of 3, meaning for every 1 unit increase in x, y increases by 3 units.