Compare Linear Functions (Tables, Graphs, and Equations)

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Front

How do you find the slope from a table of values?

Back

To find the slope from a table of values, select two points (x1, y1) and (x2, y2) and use the formula: slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept in a linear function?

Back

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

Front

How can you determine if one linear function has a greater slope than another?

Back

Compare the slope values (m) of the two functions. The function with the larger slope value has a greater slope.

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.

Front

How do you graph a linear function using its equation?

Back

To graph a linear function, identify the y-intercept (b) and plot it on the y-axis. Then use the slope (m) to find another point by rising and running from the y-intercept.

Front

What is the difference between a positive slope and a negative slope?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward line. A negative slope indicates that as x increases, y decreases, resulting in a downward line.

Front

What does it mean for two linear functions to be parallel?

Back

Two linear functions are parallel if they have the same slope but different y-intercepts. They will never intersect.

Front

What does it mean for two linear functions to be perpendicular?

Back

Two linear functions are perpendicular if the product of their slopes is -1. This means one slope is the negative reciprocal of the other.