Answer:
Slope Intercept form of the equation is [tex]y = \frac{1}{3} x - 9[/tex]
Step-by-step explanation:
Here, the two point line are given as is A(-6,-3) and B(6,-7)
The slope of the line AB = [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{-7-(-3)}{6-(-6)} = \frac{-7 + 3}{6 + 6} = \frac{4}{12} \\\implies m = \frac{1}{3}[/tex]
⇒ the slope of AB is m = (4/3)
By SLOPE INTERCEPT FORMULA:
The equation of a line with slope m and a point (x0, y0) is given as
(y-y0)= m (x-x0)
⇒ The equation of line with point (6,-7) is:
[tex]y + 7 = \frac{1}{3} (x-6) \implies 3y + 21 - x + 6 - 0\\or, -x + 3y + 27 = 0[/tex]
Now, the given equation is -x + 3y = -27
Convert it in the SLOPE INTERCEPT FORM y = mx + c
We get, 3y = x - 27
or, [tex]y = \frac{1}{3} x - \frac{27}{3} \\\implies y = \frac{1}{3} x - 9[/tex]
Hence, the Slope Intercept form of the equation is [tex]y = \frac{1}{3} x - 9[/tex]
