Finding slope from Coordinates

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually 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 from two coordinates (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-coordinate increases, the y-coordinate 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-coordinate increases, the y-coordinate decreases, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change is 0, leading to division by zero.

Front

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

Back

The slope is 2, calculated as (7 - 3) / (4 - 2).

Front

Find the slope of the line that passes through (1, 2) and (3, 6).

Back

The slope is 2, calculated as (6 - 2) / (3 - 1).

Front

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

Back

The slope is undefined, as the x-coordinates are the same.

Front

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

Back

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