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

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 $x=0$.

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

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

Final Answer