# Thread: given a linear function , find the closest point

1. ## given a linear function , find the closest point

find the point on the line y=x+1 that is closest to the point (4,1)...do i have to create the table , then sketch the graph and find out by observing or i can find it with another way?

2. Originally Posted by alessandromangione
find the point on the line y=x+1 that is closest to the point (4,1)...do i have to create the table , then sketch the graph and find out by observing or i can find it with another way?
1. find the line perpendicular to y=x+1 that passes through the point (4,1)

2. determine the point of intersection of y=x+1 and the perpendicular line found in step 1.

3. use the distance formula to find the distance between (4,1) and the point found in step 2.

3. well i applied step 1 and i applied the slope point form and i got y=x-3 then try to get the point on the intersection with y= x+1...but i cannot find it...

4. y= x- 3 is NOT perpendicular to y= x+ 1.

y= x+ 1 has slope 1. A line perpendicular to it must have slope -1.