Graphing Linear Functions

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run between two points on the line.

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1)

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the x-intercept of a line?

Back

The x-intercept is the point where the line crosses the x-axis, represented as (a, 0) in the equation y = mx + b.

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 convert the equation y = mx + b to standard form?

Back

Rearrange the equation to the form Ax + By = C by moving all terms to one side.

Front

What does the equation y = 2x represent?

Back

This equation represents a line with a slope of 2 and a y-intercept of 0, meaning it passes through the origin.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, cost per item, or growth rates.

Front

How do you determine the x and y intercepts from the equation 4x - 5y = 40?

Back

To find the x-intercept, set y = 0 and solve for x. To find the y-intercept, set x = 0 and solve for y.