Answer:
[tex]y=-\frac{x}{3}-5[/tex]
Step-by-step explanation:
Hello
we know this is a function of a line, use 2 points to find the equation
Step 1
find the slope of the line(m),using
[tex]m=\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex]
where, Point 1(X1,Y1) and point 2 (Y2,Y2) are points of the line
Let
P1=(-6,-3)
P2(6,-7)
now, replace
[tex]m=\frac{y_{2}- y_{1}}{x_{2}- x_{1}}\\m=\frac{-7-(-3)}{6-(-6)}\\m=\frac{-4}{12} \\m=-\frac{1}{3}[/tex]
Step 2
use P1 and m to find the slope-point equation
[tex]y- y_{0}}=m(x-x_{0} )\\[/tex]
Let P1(-6,-3)
m=-1/3
now, replace
[tex]y- y_{0}}=m(x-x_{0}\\y- (-3)}=-\frac{1}{3} (x-(-6))}\\y+3=-\frac{1}{3} (x+6)\\y+3=-\frac{x}{3}-2\\y=-\frac{x}{3}-2-3\\y=-\frac{x}{3}-5[/tex]
Have a great day
