Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

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

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

What is the difference between linear and non-linear functions?

Back

Linear functions create straight lines when graphed, while non-linear functions create curves or other shapes.

Front

What does it mean for a graph to be a function?

Back

A graph represents a function if every input (x-value) has exactly one output (y-value). This is often checked using the vertical line test.

Front

What is the vertical line test?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, then the graph does not represent a function.

Front

How can you determine if a table of values represents a linear function?

Back

A table represents a linear function if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What is the equation of a line with a slope of -4 and a y-intercept of 2?

Back

The equation is y = -4x + 2.

Front

If a line passes through the points (4, 3) and (19, -2), what is the slope?

Back

The slope is m = -1/3.