Graphing Standard 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

How do you convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side.

Front

What does the slope of a line represent in a graph?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What is the y-intercept in a linear equation?

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 find the x-intercept of a linear equation?

Back

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

Front

What is the significance of the coefficients in the standard form of a linear equation?

Back

The coefficients A and B determine the slope and direction of the line, while C represents the position of the line relative to the axes.

Front

Graph the equation 2x + 4y = 4. What are the intercepts?

Back

The x-intercept is (2, 0) and the y-intercept is (0, 1).

Front

Graph the equation x + y = 4. What is the slope?

Back

The slope is -1, as it can be rewritten in slope-intercept form as y = -x + 4.

Front

What is the slope of the line represented by the equation -x + 2y = 3?

Back

The slope is 0.5, as it can be rewritten in slope-intercept form as y = 0.5x + 1.5.

Front

How do you determine if two lines are parallel using their equations?

Back

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