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.
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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 \((6, 0)\).
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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 \((6, 0)\).