We know, slope of line joining two points (x₁, y₁) and (x₂, y₂) is given by(y₂-y₁)/(x₂-x₁).
Slope of line AB = (5-2)/(3-1) = 3/2
Slope of line BC = (8-5)/(7-3) = 3/4
Since slope of AB is not equal to BC so, points are not collinear.

Given equation is y=5x+10. X-intercept means value of x when y is zero
0=5x+10 => x=-2

Distance of point (x1, y1) from line ax +by +c=0 is \(|\frac{ax1+by1+c}{\sqrt{a^2+b^2}}|\).
So, distance of point (2, 4) from line 2x+y-5=0 is \(|\frac{2*2+4*1-5}{\sqrt{2^2+1^2}}| = \frac{3}{\sqrt{5}}\).

We know, slope of line joining two points (x₁, y₁) and (x₂, y₂) is given by (y₂-y₁)/(x₂-x₁).
So, slope of line joining (0, 0) and (3, 6) is (6-0)/(3-0) = 6/3 = 2.

Let general equation of line be y=m*x + c.
Given, m=4 and c=2.
=>y=4x+2

If two lines are parallel n y form same angle with positive direction of x-axis in anticlockwise direction i.e. ir inclinations are equal.

The coordinates of a point dividing line segment joining (x₁, y₁) and (x₂, y₂) externally in ratio m: n is \((\frac{mx_2-nx_1}{m-n},\frac{my_2-ny_1}{m-n})\).
So, coordinates of a point dividing line segment joining (1, 2) and (4, 5) externally in ratio 2:1 is \((\frac{2*4-1*1}{2-1},\frac{2*5-1*2}{2-1})\) = (7, 8).

We know, inclination of line is always measured with positive x-axis in anticlockwise direction.

Given equation is y=5x+10. Y-intercept means value of y when x is zero
y=0+10 => y=10

If angle between two lines with slopes m₁ and m₂ is α n tan α = |(m₁-m₂)/(1+m₁*m₂)|
tan 45° = \(|\frac{m-1/4}{1+m/4}|\)
=> \(\frac{4m-1}{m+4}\) = -1
=>- m-4 = 4m-1 => 5m = -3
=> m = -3/5.