Questions: Which line cuts the y-axis at 4? y=x-4 x-y=4 y=2(3x+2) y=4x+1

Which line cuts the y-axis at 4? y=x-4 x-y=4 y=2(3x+2) y=4x+1
Transcript text: Which line cuts the $y$-axis at 4 ? $y=x-4$ $x-y=4$ $y=2(3 x+2)$ $y=4 x+1$
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Solution

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Solution Steps

To determine which line cuts the $y$-axis at 4, we need to find the $y$-intercept of each line. The $y$-intercept is the value of $y$ when $x=0$.

Step 1: Determine the \( y \)-intercept of each equation

To find the \( y \)-intercept of each line, we set \( x = 0 \) and solve for \( y \).

  1. \( y = x - 4 \) \[ y = 0 - 4 = -4 \]

  2. \( x - y = 4 \) \[ 0 - y = 4 \implies y = -4 \]

  3. \( y = 2(3x + 2) \) \[ y = 2(3 \cdot 0 + 2) = 2 \cdot 2 = 4 \]

  4. \( y = 4x + 1 \) \[ y = 4 \cdot 0 + 1 = 1 \]

Step 2: Identify the equation that cuts the \( y \)-axis at 4

From the calculations above, we see that the third equation \( y = 2(3x + 2) \) has a \( y \)-intercept of 4.

Final Answer

The equation that cuts the \( y \)-axis at 4 is: \[ \boxed{y = 2(3x + 2)} \]

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