Writing linear equations from words y=mx+b

Front

What does the equation y = mx + b represent?

Back

It represents a linear equation where y is the dependent variable, m is the slope, x is the independent variable, and b is the y-intercept.

Front

What is the slope in the equation y = -25x + 120?

Back

The slope (m) is -25, indicating that for every increase of 1 in x, y decreases by 25.

Front

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

Back

The y-intercept (b) is the value of y when x is 0, representing the starting point of the line on the y-axis.

Front

How do you write a linear equation from a word problem?

Back

Identify the variables, determine the slope and y-intercept from the context, and then formulate the equation in the form y = mx + b.

Front

In the equation y = -0.5x + 34, what does -0.5 represent?

Back

It represents the rate at which the water level is receding, decreasing by 0.5 feet per day.

Front

If a fitness club starts with 80 members and gains 15 members each month, what is the equation for total membership?

Back

y = 15x + 80, where x is the number of months.

Front

What is the total cost equation for towing a vehicle if the service center charges $50 plus $8 per mile?

Back

C = 8m + 50, where C is the total cost and m is the number of miles.

Front

What does a negative slope indicate in a linear equation?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases.

Front

How can you identify the y-intercept from a linear equation?

Back

The y-intercept can be identified as the constant term (b) in the equation y = mx + b.

Front

What is the significance of the slope in real-world applications?

Back

The slope indicates the rate of change between two variables, showing how one variable responds to changes in another.