Linear Equation 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 unit change in x.

Front

What is the y-intercept of 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 formula to calculate the total cost in a linear equation involving fixed and variable costs?

Back

Total Cost = Fixed Cost + (Variable Cost per unit * Number of units).

Front

How can you determine the number of items purchased from a total cost?

Back

You can rearrange the total cost equation to solve for the number of items: Number of items = (Total Cost - Fixed Cost) / Variable Cost per item.

Front

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

Back

Coefficients represent the rate of change or the amount of change in the dependent variable for each unit change in the independent variable.

Front

How do you interpret the solution of a linear equation in a real-world context?

Back

The solution represents the values of the variables that satisfy the equation, often corresponding to quantities or amounts in a real-world scenario.

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. Solutions to the system are the points where the equations intersect.

Front

How do you graph a linear equation?

Back

To graph a linear equation, you can plot the y-intercept on the y-axis and use the slope to find another point, then draw a straight line through the points.