Answer:
x + 3y + 11 = 0 is the required equation.
Step-by-step explanation:
Here the given points are A( -2,-3) and B(4,-5)
Now, slope of the equation = [tex]\frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 -(-3))}{4-(-2)} = \frac{-2}{6} =-\frac{1}{3} [/tex]
Hence, the slope of the equation is m = (-1/3)
Now, by POINT SLOPE FORMULA:
The equation of a line with slope m and point (x0, y0) is given as
(y - y0) = m (x -x0)
So, here the equation of line with (4, -5) is
[tex]y - (-5) = -\frac{1}{3} (x - 4) \implies 3( y +5) = -x + 4[/tex]
or, 3y + 15 + x-4 = 0
or, x + 3y + 11 = 0
⇒ x + 3y + 11 = 0 is the required equation.
