Finding Slope

Front

What is the definition of slope?

Back

Slope is a measure of the steepness of a line, calculated 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 from 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 is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x (run) is zero.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0 because there is no change in y (rise) as x changes.

Front

If the slope of a line is 2, what does this mean in terms of rise and run?

Back

A slope of 2 means that for every 1 unit of horizontal change (run), the vertical change (rise) is 2 units.

Front

What is the slope of the line represented by the equation y = 3x + 1?

Back

The slope of the line is 3, which is the coefficient of x in the equation.

Front

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

Back

To find the slope from a table, select two points (x1, y1) and (x2, y2) and use the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line represented by the equation y = -rac{1}{2}x + 4?

Back

The slope of the line is -rac{1}{2}, which is the coefficient of x in the equation.