Equation Word Problems

A linear equation is an equation that makes a straight line when it is graphed. It can be written in the form $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

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

Identify the variables, determine the relationship between them, and express that relationship using an equation.

$$y = 12x + 35$$ , where $$y$$ is the total pages written, $$x$$ is the number of months.

Total cost can be represented as a sum of fixed costs and variable costs, often in the form $$C = F + Vx$$ , where $$C$$ is total cost, $$F$$ is fixed cost, $$V$$ is variable cost per unit, and $$x$$ is the number of units.

$$1.5x + 4y = 5050$$ , where $$x$$ is the number of children and $$y$$ is the number of adults.

Total revenue can be calculated by multiplying the price per item by the number of items sold, often expressed as $$R = P \times Q$$ , where $$R$$ is revenue, $$P$$ is price, and $$Q$$ is quantity.

$$5x + 7.5y = 60$$ , where $$x$$ is the number of cats washed and $$y$$ is the number of dogs washed.

Total cost can be calculated by adding the fixed cost to the variable cost multiplied by the number of songs, expressed as $$C = 2 + 1.29n$$ , where $$n$$ is the number of songs.