Question

Solve 0.2(x+2)=_y+_(2).

A. 0.2(x + 2) = y + 0.2
B. 0.2(x + 2) = 0.2x + 2
C. 0.2(x + 2) = y + 2

Answer 1

The correct equation is 0.2(x + 2) = y + 0.4, which simplifies to y = 0.2x + 0.4. This matches the standard linear equation form y = mx + b.

Step-by-step explanation:

To solve the equation 0.2(x+2) for y, you must first distribute the 0.2 across the parentheses. Multiplying both the x and the 2 by 0.2 gives:

0.2(x) + 0.2(2) = 0.2x + 0.4

In any standard linear equation of the form y = mx + b, we require a constant term (b) and a variable term (mx). Here, 0.2x is our variable term, and therefore, for this equation to be in linear form, y must be equal to 0.2x + some constant. The only equation that achieves this is:

0.2(x + 2) = y + 0.4, which upon solving for y, we get:

y = 0.2x + 0.4

This matches the form y = mx + b, which is characteristic of linear equations.