A line equation can be written in slope-intercept form. The slope-intercept form is
[tex]y=mx+b[/tex]Where m represents the slope and b the y-intercept.
We can substitute our points on this form to get a system of equations to find the slope and y-intercept of our desired line. Using the points (- 42.75, 5.7) and (2.75, 4.1), we have
[tex]\begin{cases}5.7=-42.75m+b \\ 4.1=2.75m+b\end{cases}[/tex]If we subtract the second equation from the first equation, we get a new equation only for the slope.
[tex]\begin{gathered} 5.7-(4.1)=-42.75m+b-(2.75m+b) \\ 1.6=-45.5m \\ m=-\frac{1.6}{45.5} \end{gathered}[/tex]And this is our slope.
