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

Front

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

Back

Identify the variables, determine the relationship between them, and express that relationship in the form of a linear equation.

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 the cost of a service based on usage?

Back

You can create a linear equation where the total cost is a function of the number of units used, typically in the form C = mx + b.

Front

What is the equation for a total cost that includes a fixed fee and a variable fee?

Back

The equation is C = fixed fee + (variable rate * number of units), where C is the total cost.

Front

How do you represent a situation where multiple items are purchased at different prices?

Back

You can use a linear equation that combines the costs of each item, such as total cost = (price of item 1 * quantity) + (price of item 2 * quantity).

Front

What is the relationship between the variables in a linear equation?

Back

The relationship is linear, meaning that as one variable increases or decreases, the other variable changes at a constant rate.