Slope: Rise over Run

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the equation of a line. It is calculated as the ratio of the rise (change in y) to the run (change in x).

Front

How is slope calculated using two points on a line?

Back

Slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

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 change in y regardless of the change in x.

Front

What is the slope of a vertical line?

Back

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

Front

If a line has a slope of 2/3, what does this mean in terms of rise and run?

Back

A slope of 2/3 means that for every 3 units of horizontal distance (run), the line rises 2 units (rise).

Front

How can you determine the slope from the equation of a line in slope-intercept form?

Back

In slope-intercept form (y = mx + b), the slope is represented by 'm'. For example, in the equation y = 2x + 1, the slope is 2.

Front

What is the slope of the line represented by the equation y = -x + 4?

Back

The slope of the line is -1, as it is the coefficient of x in the equation.

Front

How do you find the slope of a line given its graph?

Back

To find the slope from a graph, select two points on the line, determine the rise and run between them, and use the formula m = rise/run.