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 y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept (b) 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

How do you find the initial value in a linear equation?

Back

The initial value is found by identifying the y-intercept (b) in the equation y = mx + b.

Front

If a linear equation is y = 5x + 5, what is the initial value?

Back

The initial value is 5, which is the y-intercept.

Front

What is the unit rate?

Back

The unit rate is a comparison of two different quantities when they are combined together. It is often expressed as a quantity per one unit of another quantity.

Front

How do you calculate the unit rate from a total amount?

Back

To calculate the unit rate, divide the total amount by the number of units. For example, if Elijah earns $200 for 8 hours of work, the unit rate is $200 ÷ 8 = $25 per hour.

Front

What does it mean for two variables to be directly proportional?

Back

Two variables are directly proportional if they increase or decrease at the same rate, meaning their ratio remains constant.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

How can you determine if a set of points forms a linear relationship?

Back

A set of points forms a linear relationship if they can be connected by a straight line on a graph.