First, let's calculate the slope of the line:
[tex]m=\frac{6-0}{2-1}\Rightarrow m=6[/tex]Let's use a generic slope-intercept equation, the slope we just calculated and point (1, 0) as following:
[tex]\begin{gathered} y=mx+b \\ \Rightarrow0=6(1)+b \end{gathered}[/tex]Solving for b (the y-intercept):
[tex]\begin{gathered} 0=6(1)+b \\ \Rightarrow-6=b \end{gathered}[/tex]This way, we can conclude that the equation of the line in the slope-intercept form is:
[tex]y=6x-6[/tex]