The graph of the function y = kx + b intersects the coordinate axes at points A (0; -2) and B (4; 6). Find the value of k and b.

In the problem statement, it is necessary to correct “at points A (0; -2) and B (4; 6)” by “at points A (0; -2) and B (4; 0)”.

Decision.

According to the condition of the problem, the graph of the function y = kx + b intersects the ordinate axis at point A (0; -2).

Substituting the values ​​x = 0 and y = -2 in the equation of this function, we get:

-2 = k * 0 + b.

From this ratio we find b:

b = -2.

It is also known that the graph of this function crosses the abscissa at point B (4; 0).

Substituting the values ​​x = 4 and y = 0, as well as the found value b = -2 into the equation of this function, we get:

0 = k * 4 – 2.

We solve the resulting equation and find k:

k * 4 = 2;

k = 2/4;

k = 0.5.

Thus, the graph of this function intersects the coordinate axes at points A (0; -2) and B (4; 0) at k = 0.5 and b = -2.

Answer: k = 0.5; b = -2.