Given a point M (-1,2) Find the equation of a straight line passing through this point parallel

| March 3, 2021 | education

Given a point M (-1,2) Find the equation of a straight line passing through this point parallel and perpendicular to the straight line 2x-y + 3 = 0.

We write the equation of the original straight line in the following form:

2x – y + 3 = 0,

y = 2x + 3.

The formula for a parallel straight line y – y0 = k (x – x0), where k is the slope of the straight line, x0, y0 are the coordinates of the point through which the graph passes. Find the formula for a parallel line, substituting the coordinates of the point: x0 = -1, y0 = 2.

y – 2 = 2 * (x – (-1)),

y – 2 = 2x + 2,

y = 2x + 4.

The formula of the perpendicular line y – y1 = -1 / a (x – x1), where a is the slope of the line, x1, y1 are the coordinates of the point through which the graph passes.

Find the formula for a perpendicular line by substituting the coordinates of the point: x1 = -1, y1 = 2.

y – 2 = -1/2 (x + 1),

y – 2 = – 0.5x – 0.5,

y = -0.5x + 1.5.

Answer: the graph of a parallel line y = 2x + 4, a perpendicular line y = -0.5x + 1.5.



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