Slope from a Graph, Two Points and a Table

Front

What is the formula to calculate the slope of a line given 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 on a graph?

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 on a graph?

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 vertical line?

Back

The slope of a vertical line is undefined because the change in x (denominator) is zero.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0 because there is no change in y (numerator) as x changes.

Front

How do you find the slope from a graph?

Back

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

Front

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

Back

The slope represents the rate of change between two variables, which can be used to interpret trends in data, such as speed, growth rates, or costs.

Front

How can you determine the slope from a table of values?

Back

To determine the slope from a table, select two pairs of values (x1, y1) and (x2, y2), and apply the slope formula: m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line that passes through the points (1, 2) and (3, 6)?

Back

The slope is m = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

If a line has a slope of 3, what does this mean in terms of rise and run?

Back

A slope of 3 means that for every 1 unit increase in x (run), y increases by 3 units (rise).