Understanding Linear Functions and Graphs

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

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 divided by the change in x (rise over run).

Front

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

Back

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

Front

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

Back

Front

What does the y-intercept represent in a linear equation?

Back

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

Front

How do you determine if a graph is a function?

Back

To determine if a graph is a function, use the vertical line test. If any vertical line crosses the graph more than once, it is not a function.

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, indicating how much y changes for a unit change in x.

Front

How can you write an equation from a set of points?

Back

To write an equation from a set of points, find the slope using two points and then use one point to solve for the y-intercept.

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph.