Aline passes through (3, -2) and (6, 2). a. write an equation for the line in point-slope form. b. rewrite the equation in standard form using integers

(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

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