Final answer:
To find the point on the line y=6x that is closest to the point (74,0), we need to minimize the distance between the given point and any point on the line. We can achieve this by using the distance formula and finding the value of x that minimizes the distance.
Step-by-step explanation:
To find the point on the line y=6x that is closest to the point (74,0), we need to find the point on the line that has the shortest distance to the given point.
We can use the formula for the distance between two points, which is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates. In this case, the formula becomes:
distance = sqrt((x-74)^2 + (6x-0)^2)
To minimize this distance, we can take the derivative of the distance function with respect to x, set it equal to 0, and solve for x. The x-coordinate of the point on the line closest to (74,0) will be the value of x that minimizes the distance.