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 written in the form y = mx + b, where m is the slope and b is the y-intercept.

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

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 and can be expressed in terms of two variables.

Front

What does the slope represent in a linear equation?

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 unit change in x.

Front

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

Back

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

Front

How can you convert from slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms on one side and set it equal to a constant.

Front

What is the significance of the initial fee in a linear word problem?

Back

The initial fee represents a fixed cost that does not change with the number of units (like hours or items) and is often the y-intercept in the equation.

Front

How do you find the point where two linear equations intersect?

Back

To find the intersection point, solve the system of equations formed by the two linear equations simultaneously.

Front

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

Back

A real-world example is calculating the total cost of items purchased, where the cost is a linear function of the number of items bought.