Slope

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 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 a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in y as x changes.

Front

What does a negative slope indicate about the direction of a line?

Back

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

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning there is no change in x as y changes.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as 'b' in the equation y = mx + b.

Front

How can you identify the slope from the equation of a line in slope-intercept form?

Back

In the slope-intercept form of a line (y = mx + b), the slope is the coefficient 'm' of x.

Front

What is the slope of a line that rises 3 units for every 4 units it runs?

Back

The slope of the line is 3/4.

Front

If a line has a slope of -1, what does this imply about the line's angle?

Back

A slope of -1 implies that the line descends at a 45-degree angle from the horizontal.

Front

How do you determine if two lines are parallel based on their slopes?

Back

Two lines are parallel if they have the same slope.