The graph of the functions y = kx + b passes through the points A (-2; -5) and B (2; 4). Find the coefficients k and x.

A function of the form “y = kx + b” is called a linear function. The letter factors “k” and “b” are called numerical coefficients, the coefficient k is responsible for the slope of the function graph: if k> 0, then the graph is tilted to the right. The b factor is responsible for shifting the graph along the OY axis.

According to the condition of the problem, the points A (-2; -5) and B (2; 4) lie on this straight line, so their coordinates must satisfy the equation y = kx + b, using this we compose a system of equations with two unknowns:
-5 = -k + b
4 = 2k + b;

5 = k – b
4 = 2k + b;

9 = 3k
k = 3;

4 = 2 * 3 + b
b = 4 – 6
b = -2

Answer: y = 3x – 2.