How to find the equation of the straight line passing through the points M1 (1, -2) and M2 (3, 4).

General view of the equation of the straight line y = kx + b. To find the equation of the straight line (calculate the coefficients k and b) passing through the points M1 (1, -2) and M2 (3, 4), substitute the coordinates of these points into the general equation of the straight line and solve the resulting system of linear equations by the substitution method.

{k + b = -2; 3k + b = 4.

From the first equation, we express the coefficient k and substitute it into the second equation:

k = -2 – b;

3 (-2 – b) + b = 4

-6 – 3b + b = 4

-6 – 2b = 4

-2b = 4 + 6

-2b = 10

b = 10 / (-2) = -5.

k = -2 – b = -2 – 5 = -7.

So the equation of the line is y = -7x -5.