Slope and Y-Intercept

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually represented by the letter 'm'. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

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 the x-value increases, the y-value 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 the x-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation of a line y = mx + b.

Front

What is the slope of the line represented by the equation y = 4x + 2?

Back

The slope (m) is 4.

Front

What is the slope of the line represented by the equation y = -rac{1}{3}x + 5?

Back

The slope (m) is -rac{1}{3}.

Front

Find the slope of the line that passes through the points (1, 2) and (3, 6).

Back

The slope (m) is 2.

Front

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means the line is horizontal and does not rise or fall as it moves along the x-axis.

Front

If a line has an undefined slope, what does that mean?

Back

An undefined slope means the line is vertical, and it does not have a defined rise over run.