Once you know the slope, plug it into $y = mx + b$ and use one of the given points to solve for $b$, the y-intercept.

After you have the equation of the line, substitute $x = \tfrac{1}{7}$ into the equation to find the corresponding $y$-value, which is $a$.

In an expression line, type (52 - (-48))/(7 - (-18)) and note the numerical result; this is the slope of the line.

In a new expression line, type 52 = 4*7 + b and either solve it by inspection or use Desmos’s tools to see what value of b makes the equation true; this gives you the y-intercept.

Once you know the slope and intercept, type the corresponding expression for $y$ when $x = 1/7$ (for example, something like 4*(1/7) + 24 with your values) and read off the output; that output is the value of $a$. Do not round it—keep it as an exact fraction if needed.

Use the slope formula with the two points $(-18,-48)$ and $(7,52)$:

So the slope of the line is $m=4$.

Use slope-intercept form $y = mx + b$ with $m=4$.

Substitute one of the points, for example $(7,52)$:

Compute $4(7)=28$:

Subtract 28 from both sides:

So the equation of the line is $y = 4x + 24$.

The point $\left(\tfrac{1}{7}, a\right)$ lies on the line, so it must satisfy $y = 4x + 24$.

Substitute $x = \tfrac{1}{7}$:

Compute $4 \cdot \tfrac{1}{7} = \tfrac{4}{7}$, and write 24 as a fraction with denominator 7:

So

Therefore, $a = \dfrac{172}{7}$.