3-2 Rate of Change Assignment

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. 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 it mean if the slope of a line is undefined?

Back

An undefined slope occurs when a line is vertical, meaning the x-coordinates of the two points are the same (x1 = x2). In this case, the change in x is zero, leading to division by zero.

Front

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

Back

Undefined.

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

Find the slope of the line that passes through the points (1, 2) and (4, 2).

Back

0.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

If a line has a slope of 3, what does this indicate about the line's steepness?

Back

A slope of 3 indicates that for every 1 unit increase in x, the y-value increases by 3 units, making the line relatively steep.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope.

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other. If one line has a slope of m, the other line's slope will be -1/m.