Graphing Linear Functions

Front

What is the definition of slope in a linear function?

Back

The slope of a linear function is a measure of the steepness of the line, calculated as the change in y divided by the change in x (rise over run).

Front

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

Back

The slope (m) 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 does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in y as x changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

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

Back

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

Front

How do you identify the y-intercept from the slope-intercept form?

Back

In the slope-intercept form y = mx + b, the y-intercept is the value of b, which is the point where the line crosses the y-axis.

Front

What does the equation x = 2 represent on a graph?

Back

The equation x = 2 represents a vertical line that crosses the x-axis at the point (2, 0) and extends infinitely in the y-direction.

Front

How can you determine if a line is increasing or decreasing?

Back

A line is increasing if the slope is positive (rises from left to right) and decreasing if the slope is negative (falls from left to right).

Front

What is the relationship between the slope and the angle of inclination of a line?

Back

The slope of a line is equal to the tangent of the angle of inclination (θ) with respect to the positive x-axis, given by m = tan(θ).