Answer:
OPTION B: y = 6x - 27
Step-by-step explanation:
When two points on a line are given we use the following formula to determine the equation of the line:
[tex]$ \frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1} $[/tex]
where [tex]$ (x_1, y_1) $[/tex] and [tex]$ (x_2, y_2) $[/tex] are the two points on the line.
Here, the two points are [tex]$ (x_1, y_1) = (5, 3) $[/tex] and [tex]$ (x_2, y_2) = (4, -3) $[/tex].
Substituting the points in the formula, we have:
[tex]$ \frac{y - 3}{-3 - 3} = \frac{x - 5}{4 - 5} $[/tex]
[tex]$ \implies \frac{y - 3}{-6} = \frac{x - 5}{-1} $[/tex]
[tex]$ \implies y - 3 = 6x - 30 $[/tex]
∴ y = 6x - 27 is the required equation of the line.
