Linear Equations from a Table or a Graph

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 of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (upward or downward).

Front

How do you calculate the slope from a table of values?

Back

To calculate the slope from a table, use the formula: slope (m) = (change in y) / (change in x) between two points.

Front

What is the y-intercept of a linear equation?

Back

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

Front

How can you identify the slope from a graph?

Back

The slope can be identified by selecting two points on the line and calculating the rise (change in y) over the run (change in x).

Front

What does a positive slope indicate?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

How do you write the equation of a line given the slope and y-intercept?

Back

The equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The slope can represent rates of change, such as speed, cost per item, or growth rates in various contexts.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.