Finding Slope

Front

What is the formula to 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 is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

How do you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, find the rise (change in y) and run (change in x), and use the formula m = rise/run.

Front

If a line passes through the points (1, 2) and (3, 6), what is the slope?

Back

The slope is 2, calculated as (6 - 2) / (3 - 1).

Front

What is the significance of the slope in real-world applications?

Back

The slope represents the rate of change, which can be used to analyze trends, such as speed, growth, or efficiency.

Front

How can you identify the slope from an equation 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 2x - 3y = 6?

Back

To find the slope, convert to slope-intercept form: y = (2/3)x - 2, so the slope is 2/3.