Question

Find the point on the line 4x+5y−3=0 which is closest to the point (−3,−1).

Answer 1

https://www.desmos.com/calculator/ta6i5k4ymv

Answer 2

https://www.desmos.com/calculator/5dx00b0qak

Answer 3

look at both of those

Answer 4

and do what with them?

Answer 5

slope of given line=-coefficient of x/ coefficient of y=-4/5
slope of line perpendicular to the given line=-1/(-4/5)=5/4
eq.of line with slope 5/4 passing through (-3,-1) is
\[y-(-1)=\frac{ 5 }{ 4 }\left\{ x-\left( -3 \right) \right\}\]
4y+4=5x+15
-5x+4y=11
now find x and y from the given eq. and this eq.

Answer 6

can you solve it?

Answer 7

I'm not getting it right

Answer 8

First, you might want to try to estimate the x value at which the distance between the point and the line is at a minimum. Sketch a line thru the given point to the given line. Note that this new line has to be perpendicular to the given line. (Why?) Estimate (by eye) the x- and y- coordinates of the point where this new line intersects the given line. This will give you a standard by which y ou can judge whether your answer (derived via calculus) is correct or not.

Answer 9

Next, look up and review the distance formula. You want to minimize the distance from the given pt. to the given line. You could denote this distance by D.

Type out the formula for the distance D between two points: one point is (x,y), on the given line, and the other point is the given point, (-3,-1).

Answer 10

ya'll are like no help what so ever.

Answer 11

@kdancer03: Your attitude is completely inappropriate and unacceptable. Those who responded to your posted question genuinely wanted to help you. It appears that you had not done any preparation ahead of asking for help, since what was shared with you apparently made no sense to you. Don't blame your lack of preparedness on others.
...mathmale, Moderator