Finding Slope

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 (y = mx + b). It is calculated as the ratio of the change in the y-coordinate to the change in the x-coordinate between two points on the line.

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-coordinate increases, the y-coordinate 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-coordinate increases, the y-coordinate 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 the y-coordinate regardless of the change in the x-coordinate.

Front

What is the slope of a vertical line?

Back

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

Front

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

Back

Using the slope formula: m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

If a line has a slope of -3/2, what does this tell you about the line's direction?

Back

A slope of -3/2 indicates that for every 2 units the line moves to the right (positive x-direction), it moves down 3 units (negative y-direction), meaning the line falls from left to right.

Front

What is the slope of the line represented by the equation y = 4x + 1?

Back

The slope (m) is 4, as it is the coefficient of x in the slope-intercept form of the equation (y = mx + b).

Front

How can you determine the slope from a graph?

Back

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