Determining Slope from Graphs, Tables, and Two Points

Front

What is slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b).

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 is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as there is no horizontal change.

Front

If a line passes through the points (2, 3) and (4, 7), what is the slope?

Back

The slope is (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

In the context of a graph, what does the slope represent?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Front

If a line has a slope of 1/2, what does this mean in practical terms?

Back

This means that for every 2 units moved horizontally to the right, the line moves up 1 unit vertically.

Front

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

Back

The slope is 3, which indicates that for every 1 unit increase in x, y increases by 3 units.