Writing Linear Equations

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 slope (m) represent in a linear equation?

Back

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

Front

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

Back

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

Front

Write a linear equation for an object dropped from a height of 32 feet falling at 4 feet per minute.

Back

y = -4x + 32

Front

If an object is dropped from a height of 32 feet, how high will it be after 5 minutes?

Back

12 feet

Front

Write a linear equation for a train descending from 500 meters at a rate of 50 meters per minute.

Back

y = -50x + 500

Front

What is the y-intercept of the equation y = -50x + 500?

Back

500

Front

If Lisa saves $20 every week and starts with $200, what is the slope and y-intercept of her savings equation?

Back

m = 20, b = 200

Front

How do you determine the slope from a linear equation in the form y = mx + b?

Back

The slope is the coefficient of x (m) in the equation.

Front

What is the significance of a negative slope in a linear equation?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.