Recall that the slope-intercept form of an equation with slope m is:
[tex]y=mx+b.[/tex]
Now, the equation of a line that passes through (x₁,y₁), with slope m, is:
[tex]y-y_1=m(x-x_1).[/tex]
Therefore, the equation of the given line is:
[tex]y-(-1)=9(x-\frac{1}{3}).[/tex]
Taking the above equation to its slope-intercept form, we get:
[tex]\begin{gathered} y+1=9x-\frac{9}{3}, \\ y+1=9x-3, \\ y=9x-3-1, \\ y=9x-4. \end{gathered}[/tex]
Answer:
[tex]y=9x-4.[/tex]
