SLope and graphing equations

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward slant from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant from left to right.

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 (0, b) in the equation of the line y = mx + b.

Front

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

Back

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

Front

What is the equation of a line in slope-intercept form?

Back

The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a slope of zero indicate about a line?

Back

A slope of zero indicates a horizontal line, meaning there is no change in the y-value as the x-value changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the x-value remains constant while the y-value changes.

Front

How can you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and then use the formula slope = rise/run.

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, making it essential for interpreting data in various fields.