Questions: y=2x-6 y=-1/2x-6

y=2x-6 y=-1/2x-6
Transcript text: $\begin{array}{l}y=2 x-6 \\ y=-\frac{1}{2} x-6\end{array}$
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Solution

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Solution Steps

Step 1: Identify the Equations

The given equations are:

  1. \( y = 2x - 6 \)
  2. \( y = \frac{1}{2}x - 6 \)
Step 2: Find the Intersection Point

To find the intersection point of the two lines, set the equations equal to each other: \[ 2x - 6 = \frac{1}{2}x - 6 \]

Step 3: Solve for \( x \)

Subtract \(\frac{1}{2}x\) from both sides: \[ 2x - \frac{1}{2}x = -6 + 6 \] \[ \frac{4}{2}x - \frac{1}{2}x = 0 \] \[ \frac{3}{2}x = 0 \] \[ x = 0 \]

Step 4: Solve for \( y \)

Substitute \( x = 0 \) back into one of the original equations: \[ y = 2(0) - 6 \] \[ y = -6 \]

Final Answer

The intersection point of the two lines is \( (0, -6) \).

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