Algebra 1: 5.3 Rate of Change and 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 slope-intercept form of a linear equation (y = mx + b). It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

What does a zero slope indicate about a line?

Back

A zero slope indicates that the line is horizontal, meaning there is no vertical change as you move along the line.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that the line rises from left to right, meaning as the x-value increases, the y-value also increases.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line falls from left to right, meaning as the x-value increases, the y-value decreases.

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

Find the slope of the line that passes through the points (1, 2) and (3, 6).

Back

The slope is 2, calculated as (6 - 2) / (3 - 1).

Front

Find the slope of the line that passes through the points (-2, 3) and (4, -5).

Back

The slope is -4/3, calculated as (-5 - 3) / (4 - (-2)).

Front

Find the slope of the line that passes through the points (-12, -5) and (0, -8).

Back

The slope is -1/4, calculated as (-8 - (-5)) / (0 - (-12)).

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x (run) is zero, leading to division by zero.

Front

What is the slope of a horizontal line?

Back

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