Question

A line passes through (10, 3) and (13, -6). What is the equation of the line in standard form?A. 3x - y = 1B. 3x + y = 27C. 3x + y = 33D. 3x - y = 27

Answer 1

In general, given two points on a line, we can find its equation by using the formula below

`\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1) \end{gathered}`

Therefore, in our case,

`\begin{gathered} (10,3),(13,-6) \\ \Rightarrow y-3=(-6-3)/(13-10)(x-10) \\ \Rightarrow y-3=-(9)/(3)(x-10) \\ \Rightarrow y-3=-3(x-10) \\ \Rightarrow y-3=-3x+30 \\ \Rightarrow3x+y=33 \end{gathered}`

Thus, the answer is 3x+y=33, option C.