A line equation can be written in slope intercept-form, which is
![y=mx+b](https://img.qammunity.org/2023/formulas/mathematics/high-school/smsb8cbft03lwblmi49nf2l6jby2ofxzws.png)
Where m represents the slope and b the y-intercept.
If we compare our line equation
![y=(1)/(9)x+1](https://img.qammunity.org/2023/formulas/mathematics/college/1l8s5r3s87pp24xs6lzfoa99irzq5eb1zr.png)
with the slope-intercept form, we have the following correspondence
![m=(1)/(9),b=1](https://img.qammunity.org/2023/formulas/mathematics/college/f87jbe61fmkbjo80f829rew0wohrormfe1.png)
Therefore, the slope of the given line is 1/9.