Calculating Slope

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

Front

What does a zero slope indicate about a line?

Back

A zero slope indicates that the line is horizontal, meaning there is no vertical change as you move along the line.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that the line is inclined upwards from left to right, meaning as the x-value increases, the y-value also increases.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line is inclined downwards from left to right, meaning as the x-value increases, the y-value decreases.

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, leading to division by zero in the slope formula.

Front

If a line passes through the points (10, 1) and (5, 2), what is the slope?

Back

The slope is -1/5, calculated using the formula m = (2 - 1) / (5 - 10).

Front

If a line has a slope of -5/3, what does this indicate about the line's direction?

Back

This indicates that the line is decreasing, meaning as you move from left to right, the line goes down.

Front

What is the slope of a line that rises 4 units for every 3 units it runs to the right?

Back

The slope is 4/3.

Front

What is the relationship between slope and the angle of inclination of a line?

Back

The slope of a line is equal to the tangent of the angle of inclination (θ) with respect to the horizontal axis: m = tan(θ).