Make an equation of the form y = kx + in the graph of which passes through the points a (4; 4) and b (-2; -5).

If the equation takes the form y = kx + b, then the dependence on the graph will be linear. A straight line passing through 2 points is described by the equation:

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

Substitute the coordinates of points A (4; 4) and B (-2; -5) in the equation above, and express y:

(x – 4) / (-2 – 4) = (y – 4) / (-5 – 4);

(x – 4) / (-6) = (y – 4) / (-9);

(-9) * (x – 4) = (- 6) * (y – 4);

6y = 9x – 36 + 24;

y = 1.5x – 2.

Answer: the equation of the straight line y = 1.5x – 2.