Questions: Find the x - and y-intercepts of the graph of the linear equation -6 x+9 y=-18 The x-intercept is . The y-intercept is .

Find the x - and y-intercepts of the graph of the linear equation -6 x+9 y=-18 The x-intercept is . The y-intercept is .
Transcript text: Find the $x$ - and $y$-intercepts of the graph of the linear equation $-6 x+9 y=-18$ The $x$-intercept is $\square$ . The $y$-intercept is $\square$ .
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Solution

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Solution Steps

Step 1: Find the \(x\)-intercept

To find the \(x\)-intercept, set \(y = 0\) in the equation and solve for \(x\): \[ -6x + 9(0) = -18 \] \[ -6x = -18 \] \[ x = \frac{-18}{-6} = 3 \] The \(x\)-intercept is \(x = 3\).

Step 2: Find the \(y\)-intercept

To find the \(y\)-intercept, set \(x = 0\) in the equation and solve for \(y\): \[ -6(0) + 9y = -18 \] \[ 9y = -18 \] \[ y = \frac{-18}{9} = -2 \] The \(y\)-intercept is \(y = -2\).

Final Answer

The \(x\)-intercept is \(\boxed{3}\).

The \(y\)-intercept is \(\boxed{-2}\).

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