Linear Word Problems

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by the formula y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine the total cost in a linear cost model?

Back

To determine the total cost in a linear cost model, use the equation C = mx + b, where m is the variable cost per unit, x is the number of units, and b is the fixed cost.

Front

What does the slope represent in a linear equation related to cost?

Back

In a linear equation related to cost, the slope represents the rate of change in cost per unit, indicating how much the total cost increases for each additional unit.

Front

What is a fixed cost in a linear cost model?

Back

A fixed cost is a cost that does not change with the level of output or usage, such as a startup fee or monthly subscription fee.

Front

How can you find the number of months until a certain total cost is reached?

Back

To find the number of months until a certain total cost is reached, set the total cost equation equal to the desired cost and solve for the variable representing months.

Front

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

Back

The y-intercept in a linear equation represents the initial value of the dependent variable when the independent variable is zero.

Front

How do you write an equation for a situation with a constant rate of change?

Back

To write an equation for a situation with a constant rate of change, identify the initial value and the rate of change, then use the slope-intercept form: y = mx + b.

Front

What is the equation for a cell phone bill that includes a monthly fee and a per-minute charge?

Back

The equation for a cell phone bill that includes a monthly fee and a per-minute charge is C = fixed fee + (rate per minute * x), where x is the number of minutes used.

Front

How do you interpret the coefficients in a linear equation?

Back

The coefficients in a linear equation represent the rate of change (slope) and the initial value (y-intercept) of the relationship between the variables.

Front

What is the relationship between the number of hours rented and the total cost in a rental situation?

Back

In a rental situation, the total cost is typically a linear function of the number of hours rented, represented by the equation C = rate per hour * h + fixed fee.