To determine whether the point $(7, 8)$ is a solution of the equation $y = -3x + 1$, we need to substitute the values $x = 7$ and $y = 8$ into the equation and check if it holds true.

Given the equation:

$y = -3x + 1$

Substitute $x = 7$ and $y = 8$ into the equation:

$8 = -3(7) + 1$

Now, calculate the right side:

$8 = -21 + 1$ $8 = -20$

Since $8 \neq -20$, the equation does not hold. Therefore, the point $(7, 8)$ is not a solution of the equation $y = -3x + 1$.

Would you like more details or have any questions?

Here are 5 related questions you can explore:

1. How do you determine if a point is a solution to a linear equation?
2. What is the geometric meaning of checking if a point lies on the line represented by a given equation?
3. Can a point satisfy more than one linear equation at the same time?
4. How do you find the slope and intercept from the equation $y = -3x + 1$?
5. What are the methods for graphically verifying if a point lies on a line?

Tip: Always check both the $x$-value and $y$-value by substituting them into the equation to verify if the point satisfies it.