The graph of the function y = (a-1) x + a-1 crosses the abscissa axis at the point (-2; 0). Find the value of a.

From the condition, we know that the graph of the function y = (a – 1) x + a – 1 intersects the abscissa at the point (-2; 0). In order to find the value of the parameter a, we will substitute the coordinates of the point into the equation of the function and solve the resulting equation with respect to the variable a.

x = -2; y = 0;

0 = (a – 1) * (-2) + a – 1;

We solve the resulting equation:

-2 (a – 1) + a – 1 = 0;

-2 * a + 2 * 1 + a – 1 = 0;

-2a + 2 + a – 1 = 0;

Move 2 and -1 to the right side of the equation:

-2a + a = 1 – 2;

-a = -1;

a = -1: (-1);

a = 1.

Answer: a = 1.