Graphing in Standard Form and Slope Intercept Form

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

What is slope in the context of a linear equation?

Back

Slope is a measure of the steepness of a line, calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

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

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.

Front

What does the y-intercept represent in a graph?

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

How can you convert the equation 3x - y = 9 to slope-intercept form?

Back

To convert to slope-intercept form, solve for y: y = 3x - 9.

Front

What is the y-intercept of the equation y = -2x + 5?

Back

The y-intercept is 5, represented as the point (0, 5).

Front

What does a negative slope indicate about a line?

Back

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

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

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.