Key Features of Linear Functions

Front

What is the slope of a line?

Back

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

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 is the x-intercept of a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis, which occurs when y = 0.

Front

How do you find the x-intercept of the equation 4x + 2y = -12?

Back

Set y = 0 and solve for x: 4x = -12, so x = -3. The x-intercept is -3.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you determine the range from a graph?

Back

The range is found by reading the ends of the graph from bottom to top.

Front

What does it mean if a function is increasing?

Back

A function is increasing if, as x increases, the value of f(x) also increases.

Front

What does it mean if a function is decreasing?

Back

A function is decreasing if, as x increases, the value of f(x) decreases.

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.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.