Finding Slope

Front

What is the definition of slope?

Back

Slope is a measure of the steepness of a line, calculated as the ratio of the rise (vertical change) to the run (horizontal change).

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 does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating no change in y as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs with a vertical line, where the change in x is zero, leading to division by zero.

Front

If a line has a slope of -1, what does this tell you about its steepness?

Back

A slope of -1 indicates that for every unit the line rises downwards, it runs one unit to the right, creating a 45-degree angle with the horizontal.

Front

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

Back

The slope of the line is 3, which means for every 1 unit increase in x, y increases by 3 units.

Front

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

Back

The slope of the line is -rac{5}{3}, indicating a decrease in y as x increases.

Front

How can you identify the slope from a graph?

Back

The slope can be identified by selecting two points on the line, calculating the rise and run between them, and then using the formula slope = rise/run.