Linear Equations 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 (m) 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 (b) 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 find the total cost in a word problem involving multiple items?

Back

Multiply the cost of each item by the number of items purchased and sum the results to find the total cost.

Front

What is the relationship between the number of children's tickets and adult tickets sold if the total sales amount to $210?

Back

The relationship can be expressed as 3x + 7y = 210, where x is the number of children's tickets and y is the number of adult tickets.

Front

How do you represent a situation where there is a fixed cost plus a variable cost?

Back

Use the equation y = fixed cost + (variable cost per unit * number of units), such as y = 30 + 12.5x for a meal delivery.

Front

What is the equation for a budget constraint in a word problem?

Back

The equation represents the total spending limit, such as 7x + 4y = 28, where x and y are quantities of different items.

Front

How do you interpret the coefficients in a linear equation?

Back

The coefficients represent the amount of change in the dependent variable for a one-unit change in the independent variable.