Slope from a Graph, Two Points and a Table

Front

What is the formula for calculating the slope of a line?

Back

The slope (m) of a line is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

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 their coordinates, and apply the slope 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, as there is no change in the y-values regardless of the change in x-values.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in x-values is 0, leading to division by zero in the slope formula.

Front

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

Back

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

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 applied in various contexts such as speed, cost, and growth rates.

Front

How do you interpret a slope of 2 in a real-world context?

Back

A slope of 2 means that for every unit increase in the x-variable, the y-variable increases by 2 units.

Front

What is the slope of the line that passes through the points (2, 4) and (6, 12)?

Back

The slope is 2, calculated as m = (12 - 4) / (6 - 2) = 8 / 4 = 2.