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

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

The equation of a straight line passing through two points has the form

(x – x1) / (x2 – x1) = (y – y1) / (y2 – y1).

Substituting the coordinates of the points through which the straight line passes, regardless of the position of these points on the coordinate plane, we obtain the equation

(x – 2) / (0 – 2) = (y – 0) / ((-4) – 0).

You need to do the following:

– subtract numbers in brackets

(x – 2) / (-2) = y / (-4);

– multiply both sides of the equation by -4

2 (x – 2) = y;

– expand brackets

y = 2x – 4 – the desired straight line.

Answer: k = 2 and b = -4.