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Which equations are equivalent to y = 2/3x - 4 when written in slope-intercept form? Check all that apply.

A) y = 2/3x - 4

B) y = -2/3x - 4

C) y = 2/3x + 4

D) y = -2/3x + 4

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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).

User Marek Puchalski
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