Connect with a global community of knowledgeable individuals on IDNLearn.com. Join our community to access reliable and comprehensive responses to your questions from experienced professionals.
A line equation can be written in slope-intercept form, which is
[tex]y=mx+b[/tex]Where m represents the slope and b the y-intercept.
If we evaluate our points on this form, we're going to have a linear system where the solutions are those coefficients.
[tex]\begin{cases}3=8m+b \\ -6=m+b\end{cases}[/tex]If we subtract the second equation from the first, we're going to have a new equation only for the slope.
[tex]\begin{gathered} 3-(-6)=8m+b-(m+b) \\ 3+6=8m+b-m-b \\ 9=7m \\ m=\frac{9}{7} \end{gathered}[/tex]Now that we have the slope, we can use any of the equations to find the b value.
[tex]\begin{gathered} -6=(\frac{9}{7})+b \\ -6-\frac{9}{7}=b \\ b=-\frac{51}{7} \end{gathered}[/tex]Then, our line equation is
[tex]y=\frac{9}{7}x-\frac{51}{7}[/tex]And this is the graph
