Points A (1; 2) B (2; 4) C (-1; 2) are given. Write the equation of the straight line AB, write the equation of the straight lines passing through the point C parallel to AB.
The equation of the straight line passing through the 2nd points has the following form: (x – x1) / (x2 – x1) = (y – y1) / (y2 – y1). Substituting the coordinates of points A and B, we get the equation:
(x – 1) / (2 – 1) = (y – 2) / (4 – 2).
Let’s transform the equation:
x – 1 = (y – 2) / 2;
y = 2x – 2 + 2 = 2x.
General view of the equation of the straight line y = kx + b, since the required straight line is parallel to the straight line y = 2x, k = 2. Substitute the coordinates of the point C into the equation and calculate b:
2 * (-1) + b = 2;
b = 4.
Answer: the equations of the sought lines: y = 2x and y = 2x + 4.
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