Questions: What is the y-intercept in the graph of the line 3x+2y=8?

What is the y-intercept in the graph of the line 3x+2y=8?
Transcript text: What is the $y$-intercept in the graph of the line $3 x+2 y=8$ ?
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Solution

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Solution Steps

To find the $y$-intercept of the line given by the equation \(3x + 2y = 8\), we need to determine the value of \(y\) when \(x = 0\). This can be done by substituting \(x = 0\) into the equation and solving for \(y\).

Step 1: Substitute \( x = 0 \) into the equation

To find the \( y \)-intercept of the line given by the equation \( 3x + 2y = 8 \), we substitute \( x = 0 \) into the equation.

Step 2: Solve for \( y \)

Substituting \( x = 0 \) into the equation \( 3x + 2y = 8 \) gives: \[ 3(0) + 2y = 8 \] This simplifies to: \[ 2y = 8 \]

Step 3: Isolate \( y \)

To isolate \( y \), divide both sides of the equation by 2: \[ y = \frac{8}{2} = 4 \]

Final Answer

\(\boxed{y = 4}\)

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