Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

Identify the standard form of a linear equation.

1. y - y₁ = m(x - x₁)

2. y = mx + b

3. Ax + By = C

4. y = k

The correct answer is: Ax + By = C

The standard form of a linear equation is commonly expressed as Ax + By = C, where A, B, and C are integers, and A should be non-negative. This format emphasizes the relationship between the variables x and y in a linear context. It is particularly useful for quickly identifying the coefficients and constants that define the line on a coordinate plane. In the standard form, the equation represents all points (x, y) that satisfy the linear relationship defined by the coefficients A and B, which are associated with the variables x and y respectively. This form can be easily manipulated into slope-intercept form (y = mx + b) or point-slope form (y - y₁ = m(x - x₁)) if needed but is specifically recognized as the standard form. The other formats provided have different usages. The point-slope form (y - y₁ = m(x - x₁)) is useful for writing an equation of a line when you know the slope and a point on the line. The slope-intercept form (y = mx + b) is used for easily identifying the slope and y-intercept of the line. The equation y = k represents a horizontal line where y is constant, which is not the