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

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

Solution

Step 1: Identify the Equations

The given equations are:

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: \[ y = 2(0) - 6 \] \[ y = -6 \]

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

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