Slope and y-intercept

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually 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 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 does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating that there is no change in y as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in a vertical line where x remains constant, indicating that there is no change in x as y changes.

Front

What is the y-intercept in the equation of a line?

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 find the y-intercept from a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What is the slope of the line that passes through the points (-4, 7) and (-6, -4)?

Back

The slope is 11/2.

Front

What is the slope of the line that passes through the points (10, 1) and (5, 2)?

Back

The slope is -1/5.