Write the equation of a straight line that passes through two given points a (1; 3) b (5; -4).

Solution:

Canonical equation of a straight line passing through two points with coordinates

A (x1; y1) and B (x2; y2), has the form (x – x1) / (x2 – x1) = (y – y1) / (y2 – y1).

From the problem statement, we have points with coordinates a (1; 3) and in (5; -4). Let’s substitute these

data into the equation:

(x – 1) / (5 – 1) = (y – 3) / (- 4 – 3);

(x – 1) / 4 = (y – 3) / -7;

7 * (x – 1) = 4 * (y – 3);

7x – 7 = 4y – 12;

7x – 4y – 7 + 12 = 0;

7x – 4y + 5 = 0;

Answer: the desired equation of the straight line has the form 7x – 4y + 5 = 0.