Linear Equations - Word Problems - mixed

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 y-intercept represent in a linear equation?

Back

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

Front

In the equation y = mx + b, what does 'm' represent?

Back

In the equation y = mx + b, 'm' represents the slope of the line, which indicates the rate of change of y with respect to x.

Front

How do you find the total cost from a linear equation in a word problem?

Back

To find the total cost, substitute the value of x (the number of items or hours) into the equation and solve for y.

Front

If a rental cost is represented by the equation y = 120x + 250, what does the 250 represent?

Back

The 250 represents a fixed cost or initial fee that is charged regardless of the number of hours rented.

Front

Calculate the total cost if the equation is y = 2.50x + 225 and x = 400.

Back

y = 2.50(400) + 225 = 1000 + 225 = $1225.

Front

If Alan paid $790.00 for renting an event hall with the equation y = 120x + 250, how do you find the number of hours rented?

Back

Set the equation equal to 790: 790 = 120x + 250. Solve for x to find the number of hours.

Front

What is the slope in the equation y = 2.50x + 225?

Back

The slope is 2.50, which indicates that for each additional poster ordered, the total cost increases by $2.50.

Front

In the context of a word problem, what does 'x' typically represent?

Back

In word problems involving linear equations, 'x' usually represents the independent variable, such as the number of items or hours.

Front

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

Back

The solution of a linear equation provides the value of the dependent variable (y) based on a given value of the independent variable (x), which can be interpreted in the context of the problem.