Question

Which is an equation of the line that passes throughthe points (5, 2) and (10, -3)?

Answer 1

Given two points on a line, use the formula below to find its equation

`\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} (5,2),(10,-3) \\ \Rightarrow y-2=(-3-2)/(10-5)(x-5) \\ \Rightarrow y-2=-(5)/(5)(x-5) \\ \Rightarrow y-2=-(x-5)=-x+5 \\ \Rightarrow y=-x+5+2 \\ \Rightarrow y=-x+7 \end{gathered}`

Thus, the equation is y=-x+7