The straight line y = kx + b passes through the points M (2; -5) and N (0; 2). write the equation of this straight line.

In order to find the coefficients k and b of the straight line y = kx + b, if it passes through the points M (2; -5) and N (0; 2).

Let’s compose and solve the system of equations:

-5 = 2k + b;

2 = 0 * k + b;

We solve the system using the substitution method. Let us express the variable b from the first equation of the system in terms of k.

System:

b = -5-2k;

2 = -5 – 2k.

We solve the second equation of the system:

2 = – 5 – 2k;

2k = -5 – 2;

2k = -7;

k = -7/2;

k = -3.5.

System of equations:

b = -5 – 2k = -5 + 7 = 2;

k = -3.5.

Let us write down the equations of the straight line:

y = -3.5x + 2.

Answer: y = -3.5x + 2 equation of a straight line.