Slope and Y-Intercept

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

What is the formula to calculate the slope (m) between two points (x1, y1) and (x2, y2)?

Back

The formula is: 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 y = mx + b.

Front

How do you find the y-intercept from the slope-intercept form of a linear equation?

Back

In the slope-intercept form y = mx + b, the y-intercept is the value of b.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope is 2.

Front

What is the slope of the line represented by the equation y = -rac{1}{2}x + 4?

Back

The slope is -rac{1}{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.

Front

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

Back

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