We need to find where the line y equals 3x plus 1 intersects with the vertical line x equals 8. An intersection is the point where two lines cross each other on a coordinate plane.
To solve this algebraically, we substitute x equals 8 into the equation y equals 3x plus 1. This gives us y equals 3 times 8 plus 1, which equals 24 plus 1, which equals 25. Therefore, the intersection point is at coordinates 8 comma 25.
Now let's visualize this graphically. Here we see the coordinate plane with the blue line representing y equals 3x plus 1, and the red vertical line representing x equals 8. The intersection point is clearly marked at coordinates 8 comma 25, confirming our algebraic solution.
Let's verify our solution by substituting the point 8 comma 25 back into both original equations. For y equals 3x plus 1, we get 25 equals 3 times 8 plus 1, which equals 25. Check! For x equals 8, our x-coordinate is indeed 8. Check! Therefore, the intersection point is confirmed to be at coordinates 8 comma 25.