Linear Word Problems

Front

What is a linear word problem?

Back

A linear word problem is a mathematical problem that can be represented by a linear equation, typically involving relationships between two variables.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the value of y when x is 0, representing the starting point of a linear relationship on a graph.

Front

How do you identify the y-intercept in a word problem?

Back

Look for the initial amount or starting value before any changes occur.

Front

What is the general form of a linear equation?

Back

The general form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how much y increases or decreases as x increases.

Front

How can you find the point where two linear equations intersect?

Back

Set the equations equal to each other and solve for x, then substitute back to find y.

Front

What is the equation for a situation where a fixed amount is added each month?

Back

y = mx + b, where m is the amount added each month and b is the initial amount.

Front

If a family drinks 5 bottles of water per day from a case of 48 bottles, what is the equation for the number of bottles left after x days?

Back

y = 48 - 5x.

Front

In the problem about Joe’s Canoes, what does the initial fee represent?

Back

The initial fee represents the y-intercept in the cost equation.

Front

How do you set up an equation for a situation where a certain amount is spent each month?

Back

Use the equation y = -mx + b, where m is the amount spent each month and b is the initial amount.