Slope from Equation (5.01)

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness or incline of a line, typically represented as 'm' in the equation of a line, and is calculated as the change in y divided by the change in x (rise over run).

Front

How do you find the slope from the equation of a line 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 the coefficient of x, which is the slope (m).

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is zero, leading to division by zero in the slope formula.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0 because there is no change in y as x changes.

Front

Given the equation y = mx + b, what does 'm' represent?

Back

'm' represents the slope of the line, indicating how much y changes for a unit change in x.

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 the line represented by the equation y = 3x + 4?

Back

The slope of the line is 3.

Front

How can you identify the slope from the equation 4x + 2y = 12?

Back

Rearrange the equation to slope-intercept form (y = mx + b) to find the slope, which is -2.

Front

What does it mean if two lines are parallel in terms of their slopes?

Back

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

Front

What does it mean if two lines are perpendicular in terms of their slopes?

Back

If two lines are perpendicular, the product of their slopes is -1.