Standard Form of Linear Equations

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 3x = 7y - 5 into standard form?

Back

Rearranging gives 3x - 7y = -5.

Front

What are the x- and y-intercepts of the equation 5x + 3y = 15?

Back

The x-intercept is (3, 0) and the y-intercept is (0, 5).

Front

Write the standard form of the equation for the line: y = 1/4 x + 4.

Back

The standard form is x - 4y = -16.

Front

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

Back

An equation is in standard form if it is written as Ax + By = C, making it easier to identify intercepts and graph.

Front

How do you find the x-intercept of a linear equation?

Back

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

Front

How do you find the y-intercept of a linear equation?

Back

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

Front

Convert the equation 13 - 6x - y = 0 into standard form.

Back

The standard form is 6x + y = 13.

Front

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

Back

A and B determine the slope of the line; if A = 0, the line is horizontal, and if B = 0, the line is vertical.

Front

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

Back

The slope-intercept form is y = mx + b, while the standard form is Ax + By = C; both represent the same line but in different formats.