The straight line y = kx + b passes through the points A (5; 0) and B (-2; 21). Write the equation of this straight line.

Based on these conditions, we substitute the coordinates of these points into the equation of the straight line; we obtain and solve the following system of equations:

0 = 5k + b;

21 = – 2k + b;

From the first equation we express b:

b = – 5k; and substitute in the second:

21 = – 5k – 2k; we decide for k:

21 = – 7k;

k = – 21/7 = – 3.

We substitute the found value into the equation for b, and find b:

b = – 5k = – 5 * (- 3) = 15.

Now we have all the data to write the equation of the straight line:

y = – 3x + 15.

We can check:

For A (5; 0); y = (- 3) * 5 + 15 = 15 – 15 = 0; – equality is true.

At B (-2; 21); y = (- 3) * (- 2) + 15 = 6 + 15 = 21; – equality is true.