Question

Find the equation (in terms of xx ) of the line through the points (-1,3) and (2,2)

Answer 1

The equation of a line through two points (x₁,y₁) and (x₂,y₂) is given by the formula:

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

The given points are (-1,3) and (2,2).

Substitute the points (x₁,y₁)=(-1,3) and (x₂,y₂)=(2,2) into the formula:

`y-3=((2-3)/(2-(-1)))(x-(-1))`

Simplify the equation:

`\begin{gathered} y-3=(-1)/(2+1)(x+1) \\ \Rightarrow y-3=(-1)/(3)(x+1) \\ \Rightarrow y-3=-(1)/(3)x-(1)/(3) \\ \Rightarrow y=-(1)/(3)x-(1)/(3)+3 \\ \Rightarrow y=-(1)/(3)x+(8)/(3) \end{gathered}`

The required equation is y=-1/3 x+ 8/3.