Linear Equations Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that models a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the slope in a linear equation represent?

Back

The slope 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 one-unit increase in x.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It represents the starting point of the linear relationship on the y-axis.

Front

How do you write a linear equation from a word problem?

Back

Identify the variables, determine the fixed costs and variable costs, and then express the relationship in the form of a linear equation.

Front

What is the significance of the initial fee in a cost equation?

Back

The initial fee represents a fixed cost that must be paid regardless of the quantity of items or services used.

Tags

CCSS.HSF.LE.B.5

Front

How can you determine the total cost from a linear equation?

Back

Substitute the value of the independent variable (e.g., number of items or miles) into the equation to calculate the total cost.

Tags

CCSS.HSF.LE.B.5

Front

What does the equation y = mx + b represent in a real-world context?

Back

It represents a linear relationship where y is the total cost, m is the variable cost per unit, x is the number of units, and b is the fixed cost.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you interpret the coefficients in a linear equation?

Back

The coefficient of x (m) indicates the variable cost per unit, while the constant term (b) indicates the fixed cost.

Tags

CCSS.HSF.LE.B.5

Front

What is a real-world example of a linear equation?

Back

A real-world example is the cost of a cell phone plan, where the total cost is a fixed monthly fee plus a variable charge per GB of data used.

Tags

CCSS.8.EE.C.7B

Front

How do you find the amount of data used from a cell phone bill equation?

Back

Rearrange the equation to isolate the variable representing data usage (d) and substitute the total bill amount to solve for d.

Tags

CCSS.6.EE.B.7