Flashcard 1 - Finding 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

What is the formula to calculate the slope (m) between two points (x1, y1) and (x2, y2)?

Back

The formula for slope is: m = (y2 - y1) / (x2 - x1).

Front

What type of slope is represented by a line that rises from left to right?

Back

A line that rises from left to right has a positive slope.

Front

What type of slope is represented by a line that falls from left to right?

Back

A line that falls from left to right has a negative slope.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is zero.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If a line has a slope of 2, what does this indicate about the line's steepness?

Back

A slope of 2 indicates that for every 1 unit of horizontal change, the line rises 2 units vertically, making it relatively steep.

Front

Calculate the slope of the line passing through the points (1, 2) and (3, 6).

Back

Using the formula m = (y2 - y1) / (x2 - x1), the slope is m = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What is the slope of the line represented by the equation y = -3x + 4?

Back

The slope of the line is -3.

Front

If a line has a slope of 1/2, what does this mean in terms of rise and run?

Back

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