Graphing Linear Equations and Inequalities

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 (rise) over the change in x (run). It is often represented as 'm' in the equation of a 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 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 does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating that there is no change in y as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines, where x remains constant while y changes, indicating a division by zero in the slope formula.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≥ or ≤), while a dashed line indicates that the points on the line are not included (> or <).

Front

How do you graph the inequality y ≤ 2x - 4?

Back

To graph y ≤ 2x - 4, first graph the line y = 2x - 4 as a solid line, then shade below the line to represent all points where y is less than or equal to the line.

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the same as the slope, representing how much y changes for a unit change in x.

Front

How do you identify the y-intercept in the equation of a line?

Back

In the slope-intercept form of a line, y = mx + b, the y-intercept is the value of b, where the line crosses the y-axis.