# The straight line y = kx + b passes through the points A (-1; -9) and B (2; 6). Write the equations of this straight line.

To write the equation of a straight line passing through two points with known coordinates, it is necessary to substitute the coordinates of point A into the equation of the straight line, then substitute the coordinates of point B. Combine the two resulting equations into a system and solve it.

A (- 1; – 9); x = – 1; y = – 9 – substitute these numbers instead of x and y into the equation y = kx + b;

-9 = k * (- 1) + b;

B (2; 6); x = 2; y = 6 – substitute these numbers instead of x and y into the equation y = kx + b;

6 = k * 2 + b;

Let us combine the resulting equations into a system:

-9 = k * (- 1) + b; 6 = k * 2 + b;

-9 = – k + b; 6 = 2k + b – express from the first equation b through k;

b = k – 9 – substitute the expression k – 9 in the second equation of the system instead of b;

6 = 2k + k – 9;

3k – 9 = 6;

3k = 6 + 9;

3k = 15;

k = 15: 3;

k = 5 – substitute in the expression b = k – 9;

b = 5 – 9 = – 4 – substitute the values ​​of k and b into the equation of the line y = kx + b;

y = 5x + (- 4) = 5x – 4.

Answer. y = 5x – 4.

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