Graphing Linear Functions

Front

What is the definition of slope in the context of linear functions?

Back

Slope is a measure of the steepness of a line, 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 linear function?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, resulting in an upward trend.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, resulting in a downward trend.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change is 0, leading to division by zero.

Front

Given the points (2, 4) and (6, 12), what is the slope of the line passing through these points?

Back

The slope is 2, calculated as (12 - 4) / (6 - 2).

Front

If a line has a slope of -3/2, what does this tell you about the line's direction?

Back

A slope of -3/2 indicates that for every 2 units the line moves to the right, it moves down 3 units, resulting in a downward trend.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine the y-intercept from a linear equation in slope-intercept form?

Back

The y-intercept (b) is the value of y when x = 0 in the equation y = mx + b.