Question

Which equation represents a line that passes through (-9, -3) and has a slope of 6?

y-9= 6(x - 3)
y+9= 6x + 3)
y-3= 61X - 9)
y+ 3 = 6(x + 9)

Answer 1

D

Explanation:

i think

Answer 2

`\textup{\textbf{Option B}}`

Explanation:

To solve this question we will go by the options, Let us start by substituting the point the graph passes through.

(i)
`$y - 9 = 6(x - 3)$\\`

We will Substitute the point
`$(-9,-3)$` 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)
`$y + 3 = 6(x  + 9)$`

substitute
`$x = -9$` and
`$y = -3$`

We get
`$ 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.$\\`

Now to verify for the slope, we rewrite the equation in the standard form
`$ viz., y = mx + c$` where
`$m$` is the slope of the given equation.

`$ y + 3 = 6x + 54$\\$ \implies  y = 6x +54 - 3 = 6x +51$`

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.