The slopes are m1 = 2 and m2 = -1/2. The angle θ = tan⁻¹(|(m1 - m2) / (1 + m1*m2)|) = tan⁻¹(5/3), which is approximately 90 degrees.

Using the distance formula: d = √[(4 - 1)² + (6 - 2)²] = √[9 + 16] = √25 = 5.

Using the formula for distance from a point to a line, the distance is |2(1) + 3(2) - 6| / sqrt(2^2 + 3^2) = 1.

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

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

The slope m = (7 - 3) / (4 - 2) = 2. Using point-slope form: y - 3 = 2(x - 2) gives y = 2x + 1.

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

Solving the equations simultaneously, we find the intersection point is (3, 4).

'c' represents the y-intercept of the line, which is the point where the line crosses the y-axis.

Setting x = 0 in the equation gives y = 8. Thus, the y-intercept is -8.

Setting y = 0 in the equation gives 5x = 60, thus x = 12.

Rearranging to slope-intercept form gives y = -7/2x + 7, so the slope is -7/2.

Setting x = 0 in the equation gives 3y = 12, thus y = 4. The point of intersection is (0, 4).

Rearranging gives y = (4/3)x + 4. The slope is -4/3, so a parallel line has the same slope.

The slopes of the lines are -2/3 and 4. The angle θ can be found using tan(θ) = |(m1 - m2) / (1 + m1*m2)|.

The slopes are m1 = 2 and m2 = -1/2. The angle θ between the lines is given by tan(θ) = |(m1 - m2) / (1 + m1*m2)|, which results in 90 degrees.

The slopes are m1 = 3 and m2 = -1/3. The angle θ = tan⁻¹(|(m1 - m2) / (1 + m1*m2)|) = tan⁻¹(10/8) = 90 degrees.

Since parallel lines have the same slope, the equation is y - 1 = 3(x - 4) which simplifies to y = 3x - 11.

Parallel lines have the same slope. Using point-slope form: y - 2 = 3(x - 1) gives y = 3x - 1.

Since parallel lines have the same slope, the equation is y - 1 = 3(x - 2) which simplifies to y = 3x - 5.

The slope of the perpendicular line is -1/3. Using point-slope form: y - 1 = -1/3(x - 1) gives y = -1/3x + 4/3.

The slope of the perpendicular line is -1/3. Using point-slope form: y - 1 = -1/3(x - 1).

The equation of a line through the origin with slope m is y = mx. Thus, y = -3x.

Using the slope-intercept form y = mx + b, with m = -4 and b = 0, the equation is y = -4x.

Using the distance formula, length = sqrt((7-3)^2 + (1-4)^2) = sqrt(16 + 9) = 5.

The slope of the line is 4/5, so the slope of the perpendicular line is -5/4.

The slope of the line is 4/5, so the slope of the perpendicular line is -5/4.

To find the x-intercept, set y = 0. Thus, 2x = 6, giving x = 3.

To find the x-intercept, set y = 0. Thus, 4x = 20, giving x = 5.

Rearranging to y = (-2/5)x + 2, the y-intercept is 2.