Slope Flashcard_(Slope from Graphs & Equations)_C

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, 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 from two points (x1, y1) and (x2, y2)?

Back

Slope (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 slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

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

Back

In the equation y = mx + b, 'm' represents the slope of the line.

Front

What is the slope of the line represented by the equation y = 2x + 5?

Back

The slope is 2.

Front

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

Back

The slope is -3.

Front

What is the slope of the line represented by the equation 2x + 3y = 6?

Back

First, rearrange to slope-intercept form: 3y = -2x + 6, then y = -2/3x + 2. The slope is -2/3.