Linear Equations - Word Problems - mixed

Front

What is the general form of a linear equation?

Back

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

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you write an equation from a word problem involving a constant rate?

Back

Identify the initial value and the rate of change, then use the formula y = mx + b.

Front

If a line has a negative slope, what does that indicate about the relationship between x and y?

Back

A negative slope indicates that as x increases, y decreases.

Front

What is the equation of a line that passes through the point (0, 15) with a slope of 2?

Back

y = 2x + 15.

Front

How do you determine the cost from a linear equation representing a rental situation?

Back

Substitute the number of hours into the equation to find the total cost.

Front

What does the equation y = -25x + 120 represent in a real-world context?

Back

It represents a situation where a tank starts with 120 gallons of water and releases water at a rate of 25 gallons per minute.

Front

How can you find the total cost of renting an event hall for a specific number of hours?

Back

Multiply the number of hours by the hourly rate and add any fixed fees.

Front

What is the equation for Connor's lemonade sales if he starts with 15 cups and sells 5 more each hour?

Back

y = 5x + 15.