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) = ![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Substitute the given points;
![m = \frac{2-(-2)}{6-3}=\frac{2+2}{3} =\frac{4}{3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B2-%28-2%29%7D%7B6-3%7D%3D%5Cfrac%7B2%2B2%7D%7B3%7D%20%3D%5Cfrac%7B4%7D%7B3%7D)
Substitute the value of m in [1] ;
![y - (-2) = \frac{4}{3}(x-3)](https://tex.z-dn.net/?f=y%20-%20%28-2%29%20%3D%20%5Cfrac%7B4%7D%7B3%7D%28x-3%29)
......[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;
![3(y+2) = 4(x-3)](https://tex.z-dn.net/?f=3%28y%2B2%29%20%3D%204%28x-3%29)
using distributive property; ![a\cdot (b+c) = a\cdot b + a\cdot c](https://tex.z-dn.net/?f=a%5Ccdot%20%28b%2Bc%29%20%3D%20a%5Ccdot%20b%20%2B%20a%5Ccdot%20c)
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