For the equation 3x – 2y = 12, which has value of −6?AnswersA.the x-interceptB.the y-interceptC.the slopeD.the origin

To solve the problem, we need to determine what the value of −6 represents in relation to the equation $3x - 2y = 12$. We will analyze each option:

1. A. The x-intercept: The x-intercept occurs when $y = 0$. Substituting $y = 0$ into the equation gives: $3x - 2(0) = 12 \implies 3x = 12 \implies x = 4$ The x-intercept is $4$, not $-6$.

2. B. The y-intercept: The y-intercept occurs when $x = 0$. Substituting $x = 0$ into the equation gives: $3(0) - 2y = 12 \implies -2y = 12 \implies y = -6$ The y-intercept is $-6$.

3. C. The slope: To find the slope, we can rewrite the equation in slope-intercept form $y = mx + b$ where $m$ is the slope. Rearranging the equation gives: $-2y = -3x + 12 \implies y = \frac{3}{2}x - 6$ The slope $m$ is $\frac{3}{2}$, not $-6$.

4. D. The origin: The origin refers to the point $(0,0)$. This does not correspond to $-6$ in any context.

Final Answer

The value of $-6$ corresponds to B. the y-intercept.