Slopes and equations

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 rise over run, or the change in y divided by the change in x.

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 because the change in x is 0, leading to division by zero.

Front

How do you write the equation of a line in slope-intercept form?

Back

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

Front

What is the y-intercept in the equation y = 2x - 2?

Back

The y-intercept is -2, which is the value of y when x = 0.

Front

If the slope of a line is 2, what does this mean?

Back

A slope of 2 means that for every 1 unit increase in x, y increases by 2 units.

Front

What is the equation of a line with a slope of -2 that passes through the point (0, 1)?

Back

The equation is y = -2x + 1.

Front

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

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).