Finding Slope Flashcard

Front

What is the definition of slope in a linear equation?

Back

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

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates a vertical line, where the change in x is zero, leading to division by zero in the slope formula.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, where there is no change in y as x changes.

Front

If a line has a positive slope, what does this imply about the direction of the line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

If a line has a negative slope, what does this imply about the direction of the line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line is 3.

Front

Find the slope of the line that passes through the points (1, 2) and (4, 5).

Back

The slope is (5 - 2) / (4 - 1) = 3/3 = 1.

Front

What is the slope of a line that is perpendicular to a line with a slope of 2?

Back

The slope of a line perpendicular to a line with slope 2 is -1/2 (the negative reciprocal).

Front

Find the slope of the line that goes through the points (0, 17) and (19, 3).

Back

The slope is -14/19.