Linear Equation Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the variable 'y' represent in a linear function?

Back

In a linear function, 'y' typically represents the dependent variable, which is the output or the total cost in application-based problems.

Front

What is the slope in a linear equation?

Back

The slope (m) in a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Front

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

Back

The y-intercept (b) represents the value of y when x is 0. It is the starting point of the line on the y-axis.

Front

How do you interpret the y-intercept in a real-world context?

Back

The y-intercept can represent a fixed cost or initial fee in real-world scenarios, such as the starting cost before any additional expenses.

Front

What is a linear function used for in word problems?

Back

A linear function is used to model relationships between two variables, allowing us to predict outcomes based on given conditions.

Front

How do you find the cost of multiple items using a linear equation?

Back

To find the cost of multiple items, use the equation C = mx + b, where C is the total cost, m is the cost per item, x is the number of items, and b is any fixed cost.

Front

What is the significance of the points (5, 102) and (8, 150) in a linear equation?

Back

These points represent the cost of tickets for different quantities, which can be used to derive the linear equation for the total cost.

Front

How do you express a budget constraint using an inequality?

Back

A budget constraint can be expressed as an inequality, such as 700 + 125x ≤ 1400, where x represents the number of days.

Front

What does the term 'independent variable' mean in a linear equation?

Back

The independent variable (x) is the variable that represents the input or the quantity that can be controlled or changed.