Question

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Answer 1

OPTION B: y = 6x - 27

Explanation:

When two points on a line are given we use the following formula to determine the equation of the line:

`$ (y - y_1)/(y_2 - y_1) = (x - x_1)/(x_2 - x_1) $`

where
`$ (x_1, y_1) $` and
`$ (x_2, y_2) $` are the two points on the line.

Here, the two points are
`$ (x_1, y_1) = (5, 3) $` and
`$ (x_2, y_2) = (4, -3) $`.

Substituting the points in the formula, we have:

`$ (y - 3)/(-3 - 3) = (x - 5)/(4 - 5) $`

`$ \implies (y - 3)/(-6) = (x - 5)/(-1) $`

`$ \implies y - 3 = 6x - 30 $`

∴ y = 6x - 27 is the required equation of the line.