If the absorbance changes by $0.35$, how can you write an equation using the fact that $1.27$ is the change in absorbance per 1 unit of concentration?

Once you have an equation relating $0.35$ to $1.27$ and the change in concentration, isolate the change in concentration by dividing. Then round your result to the nearest hundredth.

In Desmos, type 0.35/1.27 and look at the decimal value it returns; this is the change in concentration $\Delta c$. Then, round that value to the nearest hundredth to match the answer choices.

In the linear model $A(c)=1.27c+0.04$, the coefficient $1.27$ is the slope. That means for each increase of 1 mole per liter in concentration $c$, the absorbance $A$ increases by $1.27$ units. In symbols, $1.27 = \dfrac{\Delta A}{\Delta c}$.

We are told the absorbance should increase by $0.35$ units, so $\Delta A = 0.35$.

Using $1.27 = \dfrac{\Delta A}{\Delta c}$, set up the equation

or equivalently

This equation connects the unknown concentration change $\Delta c$ to the given absorbance change.

Solve $1.27\,\Delta c = 0.35$ by dividing both sides by $1.27$:

Now compute the value:

Rounding $0.2756$ to the nearest hundredth gives $0.28$ moles per liter, which is the required increase in concentration.