SURENDRA K. answered • 06/05/15

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Adam B.

asked • 06/04/15Find the point on the line 5x+3y+1=0 which is closest to the point (–1,3).

x= ?

y=?

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SURENDRA K. answered • 06/05/15

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An experienced,patient & hardworking tutor

Slope of the line 3y+5x+1=0

is. -5/3

Slope of line perpendicular to this line is 3/5

Equation of line passing through (-1,3) and Wirth a slope 3/5

is

y-3=(3/5)(x+1)

5y-3x=18

Point of intersection of the two lines

5y-3x=18. and

5x+3y=-1

x=-177/102

y=87/34

For a check of answer----

This Point should satisfy the equation

5x+3y=-1

Timothy A. answered • 06/04/15

Tutor

4.9
(75)
I'm good at derivatives, integrals as well as application problems.

First rewrite this equation in the for y = mx + b

5x + 3y + 1 = 0 ⇒ y = (-5/3)x - 1/3

The point on this line closest the point (-1,3) should be where a perpendicular line cross this point and the line of our equation.

The equation of the perpendicular line has a slope equal to -1/m

y = (3/5)x + b

Plug in the point to find the y intersect

3 = (3/5)(-1) + b ⇒ b = 18/5

So y = (3/5)x + 18/5

Now we have to find where these two lines intersect. We two equations and two unknown.

y = (-5/3)x - 1/3

y = (3/5)x + 18/5

So, (-5/3)x - 1/3 = (3/5)x + 18/5 ⇒ (-25/15)x - 5/15 = (9/15)x + 54/15 ⇒ (-25/15 - 9/15)x = 5/15 + 54/15 ⇒

(-34/15)x = 59/15 ⇒ x = -59/34

y = (3/5)(-59/34) + 18/5 = -177/170 + 612/170 = 435/170 = 87/34

The closest point is (-59/34,87/34)

Michael J. answered • 06/04/15

Tutor

5
(5)
Mastery of Limits, Derivatives, and Integration Techniques

5x + 3y + 1 = 0 is a linear equation, we can put this in slope-intercept form.

3y = -5x - 1

y = (-5/3)x - (1/3)

Let use the slope and y-intercept of this linear function to find points on this line that is closest to the point (-1, 3).

x = 0 y = -1/3

x = -1 y = 4/3

x = -2 y = 3

x = -3 y = 14/3

If we analyze these points, we will find that the closest point is

x = -2

y = 3

You can also find the distance between the point (-1, 3) and each of the points we listed on the given line. Go with the point that has the shortest distance.

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SURENDRA K.

06/05/15