The triangle is given by the vertices A (-2; 0) B (0; 6) C (6; 1), the elimination of the height lowered

The triangle is given by the vertices A (-2; 0) B (0; 6) C (6; 1), the elimination of the height lowered from point A to the side BC has the form y = kx + b. Find k and b.

First, let’s write the equation of the line BC.

B (0; 6), C (6; 1).

The straight line equation has the form y = k * x + b. Substitute the values of the coordinates of the points into the function formula and solve the system of two equations:

6 = 0 * k + b;

1 = 6 * k + b;

b = 6;

Substitute b into the second equation:

1 = 6 * k + 6;

6 * k = -5;

k = -5/6;

y = -5/6 * x + 6 is the equation of the line on which BC lies.

The height is perpendicular to the side, so k2 = -k1 = 5/6.

y = 5/6 * x + b – height equation.

Substitute the coordinates of point A into the equation:

0 = 5/6 * (-2) + b;

b = 5/3;

y = 5/6 * x + 5/3 is the equation of height.