Question

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

Answer 1

Answer:

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

Step-by-step explanation:

We will have to find the slope of the line first

The formula for slope:

$m =\frac{y_{2}- y_{1} }{x_{2} -x_{1} } \\m= \frac{-2-2}{3-6}\\ =\frac{-4}{-3}\\ =\frac{4}{3}$

The standard form of equation of a line is:

y = mx + b

We know m,

So the equation will be:

$y= \frac{4}{3}x+b$

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,

$y = mx + b\\y = \frac{4}{3}x+(-6)\\y = \frac{4}{3} x - 6\\Multiplying\ both\ sides\ by\ 3\\3y = 4x - 18\\4x - 3y -18 = 0$ ..