Determine the sum of the parameters a and b, for which the line ax + by + 6 = 0 passes

Determine the sum of the parameters a and b, for which the line ax + by + 6 = 0 passes through the point A (-2,2) and is perpendicular to the line y = 1-0.5x

A sign of the perpendicularity of two straight lines is the dependence:

k1 = -1 / k2, where k1 = is the slope coefficient (coefficient at x) of one straight line, and k2 is the slope coefficient of the other straight line.

Let us express k1 from the formula ax + bу + 6 = 0, transforming the expression:

bу = -ax – 6;

y = (-a / b) * x – 6 / b;

k1 = -a / b.

Let us express k2 from the formula y = 1 – 0.5x:

k2 = – 0.5.

Let’s compose an expression according to the dependence of the slope coefficients and express “a” through “b”:

-a / b = -1 / (-0.5);

-a / b = 2;

a = -2b.

Substitute this expression and the coordinates of the point A (-2; 2) into the straight line formula. Let’s find the value “b”:

(-2b) * (-2) + b * 2 + 6 = 0;

4b + 2b + 6 = 0;

6b = -6;

b = -6 / 6;

b = -1.

Let’s find “a”:

a = -2 * (-1) = 2.

The sum of “a” and “b”:

2 + (-1) = 1.