Answer:
(a)
Given: A line passes through the points (3, -2) and (6, 2)
Point slope form: An equation of line passing through two points and
is given by:
.....[1] where m is the slope of the line.
Calculate first the slope of the line:
Slope(m) =
Substitute the given points;
Substitute the value of m in [1] ;
......[1]
therefore, the equation of line in point slope form is,
(b)
to find the standard form of the equation [1]
Multiply both sides by 3 in [1] we get;
using distributive property;
3y + 6 = 4x -12
Subtract 3y to both sides we get;
3y + 6 -3y = 4x - 12 - 3y
Simplify:
6 = 4x - 3y -12
Subtract 6 from both sides we get;
0 = 4x - 3y -12-6
Simplify:
4x - 3y - 18 =0
Therefore, the standard form of the equation is; 4x - 3y - 18 =0