Final answer:
To find the equation of a line perpendicular to y = -2x, find the negative reciprocal of the slope and use a point on the line to determine the y-intercept.
Step-by-step explanation:
To find an equation of a line that is perpendicular to y = -2x, we need to find the negative reciprocal of the slope of the given line. The given line has a slope of -2, so the perpendicular line will have a slope of 1/2. Let's call the equation of the perpendicular line y = mx + b. Since the slope of the perpendicular line is 1/2, we have y = (1/2)x + b. To find the value of b, we need to use a point that is on the perpendicular line.
Let's suppose we use the point (0,0) which is on the given line. Substituting the coordinates of the point into the equation of the perpendicular line, we have 0 = (1/2)(0) + b. Simplifying this equation, we get 0 = 0 + b, so b = 0.
Therefore, the equation of the line perpendicular to y = -2x is y = (1/2)x.
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