Finding Slope and Line Equations

Front

What is the slope of a line?

Back

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

Front

What is the slope-intercept form of a line?

Back

The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

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 positive slope indicate about a line?

Back

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

Front

What does a negative slope indicate about a 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 a horizontal line?

Back

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

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it would require division by zero in the slope formula.

Front

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

Back

If two lines are perpendicular, the product of their slopes is -1. If one slope is m, the other slope is -1/m.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form y = mx + b.

Front

Given the equation y = 3x + 5, what is the slope?

Back

The slope (m) is 3.