Writing Equations in Standard Form from Graphs

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 slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms involving x and y on one side and the constant on the other.

Front

What does it mean for an equation to be in standard form?

Back

An equation is in standard form when it is written as Ax + By = C, with A, B, and C as integers, and A is non-negative.

Front

What is the first step in writing an equation in standard form from a graph?

Back

Identify the slope (m) and the y-intercept (b) from the graph.

Front

If a line has a slope of -3/4, what is the corresponding standard form equation?

Back

An example of a standard form equation with a slope of -3/4 could be 3x + 4y = 16.

Front

What is the significance of the coefficients A and B in the standard form Ax + By = C?

Back

The coefficients A and B determine the orientation and steepness of the line represented by the equation.

Front

How can you determine the x-intercept from a standard form equation?

Back

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

Front

How can you determine the y-intercept from a standard form equation?

Back

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

Front

What is the relationship between the slope and the standard form of a linear equation?

Back

The slope can be derived from the standard form by rearranging the equation into slope-intercept form (y = mx + b).

Front

What is an example of a standard form equation with integer coefficients?

Back

An example is 2x + 3y = 6.