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.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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.

Tags

CCSS.HSF-LE.A.1B

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.

Tags

CCSS.HSF.LE.B.5

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.7.EE.B.4A

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.

Tags

CCSS.HSF.LE.B.5

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.HSF.LE.B.5

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.

Tags

CCSS.8.EE.B.5