Calculating Slope of a Line

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you calculate the slope of a line given 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 slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If a line rises from left to right, what type of slope does it have?

Back

The line has a positive slope.

Front

If a line falls from left to right, what type of slope does it have?

Back

The line has a negative slope.

Front

Find the slope of the line that passes through the points (2, 3) and (4, 7).

Back

m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

Find the slope of the line that passes through the points (1, 2) and (3, 2).

Back

m = (2 - 2) / (3 - 1) = 0 / 2 = 0.

Front

Find the slope of the line that passes through the points (5, 5) and (5, 10).

Back

The slope is undefined because the x-coordinates are the same.

Front

What does a slope of -1 indicate about a line?

Back

A slope of -1 indicates that for every unit increase in x, y decreases by 1 unit, resulting in a downward slant from left to right.