Questions: Find an equation of the line L. L is perpendicular to y=-2x.

Transcript text: Find an equation of the line $L$. $L$ is perpendicular to $y=-2 x$.

Solution

Solution Steps

Step 1: Identify the Slope of the Given Line

The slope of the given line is $m = -2$.

Step 2: Calculate the Slope of the Perpendicular Line $L$

The slope of a line perpendicular to another line with slope $m = -2$ is $-\frac{1}{m} = 0.5$.

Step 3: Use a Point on the Line $L$ or Assume the Y-intercept of Line $L$ to be $b'$

For simplicity, we assume the y-intercept of line $L$ to be $b' = 0$.

Step 4: Formulate the Equation of Line $L$

With the slope of line $L$ known to be $-\frac{1}{m} = 0.5$ and assuming its y-intercept is $b' = 0$, the equation of line $L$ can be written as $y = 0.5x + 0$.

Final Answer:

The equation of the line $L$ that is perpendicular to the given line $y = -2x + b$ is "y = 0.5x + 0".

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