Answer:
(2,10)
Explanation:
Whenever you want to find the point that is closest, it will always be perpendicular to the line
This is because the perpendicular line is the shortest distance to a point (it will make 90 degrees with the line)
So
In order to find the slope of the perpendicular line, you take the slop and you do the negative reciprocal of it.
In this case:
the slope is 5
So:
the negative reciprocal is -1/5
Now we know the slope of the line that will be made by point P to intersect with y=5x
Then, you use the equation:
y=mx+b
and plug in the numbers that you know which is the y coordinate, x coordinate, and slope to find the y-intercept:
0 = -1/5(52) + b
b = 52/5
Finally, set the equations equal to each other to find the point that the perpendicular line intersects y=5x
5x = -1/5x + 52/5
x = 2
then to find the y coordinate you plug the x back into the equation:
y = 5(2)
y = 10
So the answer is (2,10)