The equation y = 2x + 1, when expressed using integers, remains as is. When expressed with proper fractions, it becomes y = (2/1)x + (1/1), and using improper fractions, it is y = (2/1)x + (1/1).
The given equation of the line in slope-intercept form is y = 2x + 1. To express this equation using integers, proper fractions, and improper fractions in simplest form, let's break it down.
Using integers: The given form, y = 2x + 1, is already expressed with integers.
Using proper fractions: We can rewrite the equation by expressing the constants as fractions with a denominator of 1. Therefore, y = (2/1)x + (1/1). This form preserves the original equation's meaning while using proper fractions.
Using improper fractions: In the expression (2/1)x + (1/1), the term (2/1)x can be viewed as an improper fraction, as the coefficient 2 can be written as 2/1. Therefore, the equation in this form is y = (2/1)x + (1/1).
All three forms convey the same linear relationship, with the choice of representation depending on the context and preference.