Linear 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 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 steep the line is.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you write an equation for a total cost that includes a fixed fee and a variable fee?

Back

The equation is written as y = fixed fee + (variable fee per unit * number of units).

Front

If a car rental company charges a flat fee plus an hourly rate, how would you express the total cost for x hours?

Back

Total cost = flat fee + (hourly rate * x).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is slope-intercept form?

Back

Slope-intercept form is a way of writing a linear equation as y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine if a situation can be modeled by a linear equation?

Back

A situation can be modeled by a linear equation if it involves a constant rate of change between two variables.

Front

What is the difference between slope-intercept form and standard form?

Back

Slope-intercept form emphasizes the slope and y-intercept, while standard form is a more general representation of a linear equation.

Front

How would you model a situation where a person earns money based on the number of tasks completed?

Back

You would use a linear equation where the total earnings = base pay + (pay per task * number of tasks).