Final answer:
The equation equivalent to y = 2/3x - 4 in slope-intercept form is A) y = 2/3x - 4. Other options have different slopes or y-intercepts, making them not equivalent to the original equation.
Step-by-step explanation:
The question asks which equations are equivalent to y = 2/3x - 4 when written in slope-intercept form. To compare, we look at the slope and y-intercept values. The slope-intercept form is written as y = mx + b, where m is the slope and b is the y-interceptor. Looking at the given equations:
- A) y = 2/3x - 4: This has the same slope (2/3) and the same y-intercept (-4) as the original equation, so it is equivalent.
- B) y = -2/3x - 4: The slope here is negative (-2/3) and thus not equivalent to the original equation's positive slope (2/3).
- C) y = 2/3x + 4: The y-intercept here is +4, which is the opposite of the original equation's y-intercept (-4), so it is not equivalent.
- D) y = -2/3x + 4: Both the slope (-2/3) and y-intercept (+4) are different from the original equation, making it not equivalent.
Therefore, the only equation equivalent to y = 2/3x - 4 is option A).