Linear Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that models a straight line when graphed. It can be expressed in various forms, including slope-intercept form (y = mx + b) and standard form (Ax + By = C).

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

What is standard form of a linear equation?

Back

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

Front

How do you determine whether to use slope-intercept form or standard form for a linear equation?

Back

Use slope-intercept form when you need to identify the slope and y-intercept directly. Use standard form when you want to express the equation in a way that is easier for certain applications, such as finding intercepts.

Front

What does the slope of a line represent in a real-world context?

Back

The slope represents the rate of change between two variables in a real-world context, indicating how much one variable changes for a unit change in another variable.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

Front

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

Back

Identify the variables, determine the relationship between them, and translate the information into a mathematical equation.

Front

What is the significance of the initial fee in a linear cost model?

Back

The initial fee represents a fixed cost that does not change with the quantity of the variable, affecting the total cost calculation.

Front

How do you interpret the coefficients in a linear equation?

Back

Coefficients represent the rate of change or the cost per unit of the variable in the context of the problem.

Front

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

Back

An example is the equation for a cell phone bill: C = 0.20x + 15, where C is the total cost, x is the number of minutes used, 0.20 is the cost per minute, and 15 is the base monthly fee.