Finding Slope of a Line

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

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 does a positive slope indicate about a line?

Back

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

Front

What does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating that there is no vertical change as the x-value changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines where the x-values are constant, resulting in a division by zero in the slope formula.

Front

If a line has a slope of 4, what does this mean in terms of rise and run?

Back

A slope of 4 means that for every 1 unit of horizontal change (run), the vertical change (rise) is 4 units.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line is 3.

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 slope formula m = rise/run.

Front

What is the slope of a line that is perfectly vertical?

Back

The slope of a perfectly vertical line is undefined.