Question

A line passes through (3, -2) and (6,2). Write an equation for the line in point-slope form.

Rewrite the equation in standard form using integers.

Answer 1

4x - 3y -18 = 0 or y = 4x/3 - 6

Explanation:

We will have to find the slope of the line first

The formula for slope:

`m =(y_(2)- y_(1) )/(x_(2) -x_(1) ) \\m= (-2-2)/(3-6)\\ =(-4)/(-3)\\ =(4)/(3)`

The standard form of equation of a line is:

y = mx + b

We know m,

So the equation will be:

`y= (4)/(3)x+b`

We have to find the value of b, for that we will put any one of the point in the equation

So, putting (6,2)

2 = 4/3 * 6 + b

2 = 8 +b

b = -6

Putting the value of m and b in the standard form of equation of line,

`y = mx + b\\y = (4)/(3)x+(-6)\\y = (4)/(3) x - 6\\Multiplying\ both\ sides\ by\ 3\\3y = 4x - 18\\4x - 3y -18 = 0` ..