Graphing and Slope Review

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, typically represented 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-values increase, the y-values also increase, 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-values increase, the y-values decrease, 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 vertical change as the x-values change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as there is no horizontal change.

Front

Given the points (2, 3) and (4, 7), find the slope.

Back

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

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

Back

The slope is 3, which indicates that for every unit increase in x, y increases by 3 units.

Front

How do you identify the slope from the equation of a line in slope-intercept form (y = mx + b)?

Back

The slope (m) is the coefficient of x in the equation.

Front

What is the slope of the line represented by the equation 2y - 4x = 8?

Back

First, rewrite in slope-intercept form: y = 2x + 4. The slope is 2.