Final answer:
To find the equation for the line passing through a point and perpendicular to a given line, we find the negative reciprocal of the slope of the given line and use the point-slope form of a line.
Step-by-step explanation:
To find an equation for the line passing through the point (2,-5) and perpendicular to the line y=5x-18, we know that the slope of the new line will be the negative reciprocal of the slope of the given line. The given line has a slope of 5, so the perpendicular line will have a slope of -1/5. Using the point-slope form of a line, we can write the equation as: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point. Plugging in the values, we have:
y - (-5) = -1/5(x - 2)
Expanding and simplifying, the equation for the line is y = -1/5x - 3.4.
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