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 much y changes for a one-unit increase in x.

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

How do you convert a linear equation from slope-intercept form to standard form?

Back

Rearrange the equation y = mx + b to the form Ax + By = C by moving all terms involving variables to one side.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients indicate the relationship between the variables. The coefficient of x (slope) shows the rate of change, while the constant term (y-intercept) shows the starting value.

Front

How can you determine the number of solutions to a linear equation?

Back

A linear equation can have one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (same line).

Front

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

Back

A real-world example is calculating the total cost of items: if each item costs $5, the total cost for x items can be represented as y = 5x.

Front

How do you find the total cost in a linear equation involving fixed and variable costs?

Back

The total cost can be found by adding the fixed cost to the variable cost multiplied by the number of items: y = fixed cost + (variable cost per item * number of items).