Linear Relationships

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y (vertical) divided by the change in x (horizontal).

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

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

Front

What is the slope of the line that crosses through the points (0, 2) and (-10, -16)?

Back

9/5.

Front

What is the slope of the line with the equation y = 4x + 12?

Back

4.

Front

What is a proportional relationship in terms of linear equations?

Back

A proportional relationship is a linear relationship that passes through the origin (0,0).

Front

Does the graph of a line that does not pass through the origin represent a proportional relationship?

Back

No, because it does not go through the origin.

Front

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

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the equation of the line shown if it has a slope of 1/4 and a y-intercept of 20?

Back

y = 1/4x + 20.