Question

Write an equation of a line that passes through (-1,3)and (1,4)

Answer 1

We want to write an equation of a line that passes through (-1,3) and (1,4)

First, let us find the slope m of the line for the points (-1,3) and (1,4)

We have

`\begin{gathered} m=(4-3)/(1-(-1)) \\ m=(1)/(1+1) \\ m=(1)/(2) \end{gathered}`

Now, equation of a line in point slope form becomes

`\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(-1,3) \end{gathered}`

plugging in the values, we have

`\begin{gathered} y-y_1=m(x-x_1) \\ y-3=(1)/(2)(x-(-1) \\ y-3=(1)/(2)(x+1) \\ y-3=(1)/(2)x+(1)/(2) \\ y=(1)/(2)x+(1)/(2)+3 \\ y=(1)/(2)x+(7)/(2) \end{gathered}`

Hence the answer becomes

`y=(1)/(2)x+(7)/(2)`