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SOLUTION

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

[tex]\begin{gathered} m=\frac{4-3}{1-(-1)} \\ m=\frac{1}{1+1} \\ m=\frac{1}{2} \end{gathered}[/tex]

Now, equation of a line in point slope form becomes

[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(-1,3) \end{gathered}[/tex]

plugging in the values, we have

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

Hence the answer becomes

[tex]y=\frac{1}{2}x+\frac{7}{2}[/tex]

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