Slope (Parallel and Perpendicular Lines)

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 divided by the change in x (rise/run).

Front

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

Back

The slope (m) can be 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 two lines are parallel, what can be said about their slopes?

Back

If two lines are parallel, they have the same slope.

Front

If two lines are perpendicular, how are their slopes related?

Back

If two lines are perpendicular, the product of their slopes is -1 (m1 * m2 = -1).

Front

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

Back

The slope of the line is 3.

Front

How do you find the slope from a linear equation in standard form (Ax + By = C)?

Back

To find the slope from the standard form, rearrange the equation into slope-intercept form (y = mx + b) and identify 'm'.

Front

What is the slope of the line that passes through the points (2, 3) and (4, 7)?

Back

The slope is (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

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

Back

A slope of -1 indicates that the line descends at a 45-degree angle from left to right.