Graphing Linear Equations

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line. It is calculated as the change in y (rise) divided by the change in x (run).

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as 'b' in the slope-intercept form of a line equation, y = mx + b.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

How can you identify the y-intercept from an equation?

Back

In the equation y = mx + b, the y-intercept is the value of b.

Front

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

Back

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

Front

How do you graph a linear equation using the slope and y-intercept?

Back

Start at the y-intercept on the y-axis, then use the slope to determine the rise over run to plot additional points.

Front

What is the relationship between parallel lines and their slopes?

Back

Parallel lines have the same slope but different y-intercepts.