Which is the graph of 2 x minus 3 y equals 12?

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(1 point)
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A line is shown on a coordinate grid passing through points left-parenthesis 0 comma 4 right-parenthesis and left-parenthesis negative 6 comma 0 right-parenthesis.
Image with alt text: A line is shown on a coordinate grid passing through points left-parenthesis 0 comma 4 right-parenthesis and left-parenthesis negative 6 comma 0 right-parenthesis.

A line is shown on a coordinate grid passing through points left-parenthesis 0 comma negative 4 right-parenthesis and left-parenthesis negative 6 comma 0 right-parenthesis.
Image with alt text: A line is shown on a coordinate grid passing through points left-parenthesis 0 comma negative 4 right-parenthesis and left-parenthesis negative 6 comma 0 right-parenthesis.

A line is shown on a coordinate grid passing through points left-parenthesis 0 comma negative 4 right-parenthesis and left-parenthesis 6 comma 0 right-parenthesis.
Image with alt text: A line is shown on a coordinate grid passing through points left-parenthesis 0 comma negative 4 right-parenthesis and left-parenthesis 6 comma 0 right-parenthesis.

A line is shown on a coordinate grid passing through points left-parenthesis 0 comma 4 right-parenthesis and left-parenthesis 6 comma 0 right-parenthesis.
Image with alt text: A line is shown on a coordinate grid passing through points left-parenthesis 0 comma 4 right-parenthesis and left-parenthesis 6 comma 0 right-parenthesis.
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Answer 1

To find the graph of the equation \(2x - 3y = 12\), we can determine its x-intercept and y-intercept, which will help us plot the line.

1. Finding the x-intercept: Set \(y = 0\) in the equation. \[ 2x - 3(0) = 12 \implies 2x = 12 \implies x = 6 \] So, the x-intercept is at the point \((6, 0)\).

2. Finding the y-intercept: Set \(x = 0\) in the equation. \[ 2(0) - 3y = 12 \implies -3y = 12 \implies y = -4 \] So, the y-intercept is at the point \((0, -4)\).

Now we can summarize the intercepts:

• The x-intercept is \((6, 0)\)
• The y-intercept is \((0, -4)\)

Based on the options provided, the correct graph is the one that passes through the points \((0, -4)\) and \((6, 0)\):

Response: A line is shown on a coordinate grid passing through points \((0, -4)\) and \((6, 0)\).