Study Guide Unit 4

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be tested using the vertical line test on a graph.

Front

What does the equation y = -x + 2 represent?

Back

This equation represents a linear function with a slope of -1 and a y-intercept of 2. It describes a line that decreases as x increases.

Front

What is the difference between a relation and a function?

Back

A relation is a set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Front

How do you write the equation of a line given its slope and y-intercept?

Back

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

Front

What is the slope of the line represented by the equation y = 1/3x - 2?

Back

The slope of the line is 1/3.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the line falls from left to right.

Front

What is the y-intercept in the equation y = -3x + 4?

Back

The y-intercept is 4, which is the point where the line crosses the y-axis.

Front

How can you find the slope from two points on a line?

Back

The slope can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.