Answer:
[tex]\textup{\textbf{Option B}}[/tex]
Step-by-step explanation:
To solve this question we will go by the options, Let us start by substituting the point the graph passes through.
(i) [tex]$y - 9 = 6(x - 3)$\\[/tex]
We will Substitute the point [tex]$(-9,-3)$[/tex] to check if it satisfies the equation. Since, it does not we will move to the second equation.
We repeat this for the remaining three options.
For (iv) [tex]$y + 3 = 6(x + 9)$[/tex]
substitute [tex]$x = -9$[/tex] and [tex]$y = -3$[/tex]
We get [tex]$ L.H.S. = y + 3 = -3 + 3 = 0 $\\$ R.H.S. = 6(x + 9) = 6(-9 + 9) = 0$\\$ \therefore L.H.S. = R.H.S.$\\[/tex]
Now to verify for the slope, we rewrite the equation in the standard form [tex]$ viz., y = mx + c$[/tex] where [tex]$m$[/tex] is the slope of the given equation.
[tex]$ y + 3 = 6x + 54$\\$ \implies y = 6x +54 - 3 = 6x +51$[/tex]
Comparing it with the standard form, we get the slope of the line to be equal to 6. Hence, Option 4 would be the correct answer.
