Slope Basics

Front

What is the definition of slope?

Back

Slope is a measure of the steepness of a line, calculated as the ratio of the vertical change to the horizontal change between two points on the line.

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, indicating no vertical change as the x-value changes.

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

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

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

Back

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

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

What is a proportional relationship in terms of slope?

Back

A proportional relationship has a constant slope that passes through the origin (0,0), meaning it can be expressed as y = kx, where k is a constant.