The slope m = (4 - 2) / (3 - 1) = 1. Using point-slope form, y - 2 = 1(x - 1) gives y = x + 1.

The slope m = (6 - 2) / (3 - 1) = 2. Using point-slope form, y - 2 = 2(x - 1) gives y = 2x.

The equation of a line through the origin with slope m is y = mx. Thus, y = -5x.

The equation of a line through the origin with slope m is y = mx. Thus, y = -1x or y = -x.

Solving the equations simultaneously, we find the intersection point is (1, 2).

Solving the equations simultaneously, we find x = 2 and y = 3. Thus, the point of intersection is (2, 3).

Setting 2x + 1 = -x + 4 gives 3x = 3, thus x = 1. Substituting back, y = 2(1) + 1 = 3. The intersection is (1, 3).

Setting 3x + 1 = -x + 5 gives 4x = 4, thus x = 1. Substituting x back gives y = 4. The intersection point is (1, 4).

The slope of the line 3x + 4y = 12 is -3/4. The slope of the perpendicular line is the negative reciprocal, which is 4/3.

The slope of the line 4x + 3y = 12 is -4/3. The slope of the perpendicular line is the negative reciprocal, which is 3/4.

The slope of the line is -5/2. The slope of the perpendicular line is the negative reciprocal, which is 2/5.

The slope of the line is 7/2. The slope of the perpendicular line is the negative reciprocal, which is -2/7.

The slope of the line is 7/2. The slope of the perpendicular line is the negative reciprocal, which is -2/7.

The slope m = (9 - 5) / (6 - 4) = 4/2 = 2.

Setting y = 0 in the equation gives 5x + 10 = 0, thus x = -2.

Setting y = 0 in the equation gives 6x = 12, thus x = 2. The x-intercept is 2.

Setting x = 0 in the equation gives 5y = 20, thus y = 4. The y-intercept is 4.

The slope of the given line is 3. The slope of a line perpendicular to it is -1/3.

Substituting (0, -4) into the equation gives 4(0) - 5(-4) + 20 = 0, which is true.