# Write the equation of the straight line AB, if A (-7; 1), B (14; 4).

July 29, 2021 | education

| We will use the fact that the equation of a straight line that passes on the coordinate plane through two points with coordinates (x1; y1) and (x2; y2) for x1 ≠ x2 and y1 ≠ y2 can be written in the following form:

(x – x1) / (x2 – x1) = (y – y1) / (y2 – y1).

According to the problem statement, point A has coordinates (-7; 1), and point B has coordinates (14; 4).

Substituting the values x1 = -7, y1 = 1, x2 = 14 and y2 = 4 into the general equation of the straight line, we get:

(x – (-7)) / (14 – (-7)) = (y – 1) / (4 – 1).

Simplifying this ratio, we get:

(x + 7) / 21 = (y – 1) / 3;

3 * (x + 7) = 21 * (y – 1);

x + 7 = 7 * (y – 1);

x + 7 = 7y – 7;

x – 7y + 7 + 7 = 0;

x – 7y + 14 = 0.

Answer: x – 7y + 14 = 0.

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