Final answer:
Graph the equations y = x + 1 and y = -x + 7. The intersection of the two lines, found by setting the equations equal to each other, provides the heated focal point, which is at (3,4).
Step-by-step explanation:
To find the heated focal point created by two intersecting laser beams described by the equations y = x + 1 and y = -x + 7, we first graph both lines.
The point where they intersect will be the focal point where the heat is concentrated.
Step 1: Plotting the first line, y = x + 1, we can start with the y-intercept at (0,1) and use the slope of 1 to rise 1 unit and run 1 unit to find other points on the line.
Plotting several points, we can then draw the line.
Step 2: Plotting the second line, y = -x + 7, we begin at the y-intercept at (0,7) and use the slope of -1 to fall 1 unit and run 1 unit to the right to identify additional points. Plot this line on the same graph.
Step 3: The intersection point of these two lines is the solution to the system of equations, representing the heated focal point.
Solving the system algebraically by setting the equations equal to each other, we get x + 1 = -x + 7, which simplifies to 2x = 6, so x = 3.
Substituting x = 3 into either equation gives y = 4.
Therefore, the focal point is at (3,4).