The equation of a line is given by:
[tex]y-y_1=m(x-x_1)[/tex]
where (x1,y1) is a point on the line and m is the slope. To find the slope of a line we use the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
In this case, we have:
[tex]m=\frac{4-3}{5-(-2)}=\frac{1}{5+2}=\frac{1}{7}[/tex]
Then, the equation of the line is:
[tex]\begin{gathered} y-4=\frac{1}{7}(x-5) \\ 7y-28=x-5 \\ x-7y=-23 \end{gathered}[/tex]
Therefore:
[tex]x-7y=-23[/tex]
