Line y = kx + b passes through points A (4, -6) and B (-8. – 12). Find k and b and write down the equation of this line.

A (4; – 6); x = 4; y = – 6 – substitute these numbers instead of x and y into the equation y = kx + b;
-6 = k * 4 + b;

B (- 8 ;. – 12); x = – 8; y = – 12 – substitute these numbers instead of x and y into the equation y = kx + b;
-12 = k * (- 8) + b;

Let us combine the resulting equations into a system:

-6 = k * 4 + b; -12 = k * (- 8) + b;

-6 = 4k + b; – 12 = – 8k + b – we express from the second equation b through k;

b = 8k – 12 – substitute the expression 8k – 12 instead of b in the first equation of the system;

-6 = 4k + 8k – 12;

12k – 12 = – 6;

12k = – 6 + 12;

12k = 6;

k = 6: 12;

k = 1/2 – substitute in b = 8k – 12;

b = 8 * 1/2 – 12 = 4 – 12 = – 8 – substitute the values of k and b into the equation of the straight line y = kx + b;

y = 1 / 2x + (- 8) = 0.5x – 8.

Answer. y = 0.5x – 8.