The graph of the function y = kх + m passes through point A (2; 5) and crosses the OY

The graph of the function y = kх + m passes through point A (2; 5) and crosses the OY axis at point (0; -3). Find the value of the coefficients k and m.

If the straight line y = kx + m passes through the point O (x1; y1), then the following relation is true:

y1 = k * x1 + m.

According to the condition of the problem, the straight line y = kx + m passes through the point A (2; 5), therefore, the following relation is true:

5 = k * 2 + m.

It is also known that this line passes through the point B (0; -3), therefore, the following relation is true:

-3 = k * 0 + m.

We solve the resulting system of equations.

From the second equation follows:

m = -3.

Substituting the found value m = -3 into the equation 5 = k * 2 + m, we get:

5 = k * 2 – 2;

k * 2 = 5 + 2;

k * 2 = 7;

k = 7/2;

k = 3.5.

Answer: m = -3; k = 3.5.