Write the equation of the line that is perpendicular to the line 8y−16=5x 8y−16=5x through the point (5,-5).

Question

this question has me confused and id like good answers because this is for an important matter.

Answer 1

A line (y=mx+b) that is perpendicular to the given line (8y-16=5x) will have a slope that's reversed.

 

If the slope of the given line is "m" then the perpendicular line will have a slope of "-1/m".

So first solve for the slope of the given line.

8y-16=5x

8y = 5x+16

y = (5/8)x + 2

 

The slope of the given line is 5/8

The new equation you write for the perpendicular line will have a slope of -8/5  

 

 

The point (5,-5) will give you the y-intercept, b

 

Here's what you have so far..

 

y = (-8/5)x + b

 

plug in the point (5,-5) for (x,y) and solve for b

 

-5 = (-8/5)*(5) + b

-5 = -8 + b

-5 + 8 = b

3 = b

 

put the y-intercept into your line equation.

 

y = (-8/5)x + 3

Answer 2

Write the given line in slope-intercept, or y = mx + b form

 

8y - 16 = 5x

 

8(y - 2) = 5x

 

y - 2 = (5/8)x

 

y = (5/8)x + 2

 

In the equation y = mx + b, m = the slope of the line and b = the y-intercept

 

The slope of the given line is 5/8. A line perpendicular to this one will have a negative reciprocal slope, which is -8/5. Since we are told that this line must pass through the point (5, 5), we can let these represent x and y, respectively, in the slope-intercept form of the equation of a line.

 

-5 = (-8/5)(5) + b

 

-5 = -8 + b

 

b = 3

 

The equation of the line perpendicular to 8y - 16 = 5x is:

 

y = (-8/5)x + 3

 

If we wanted to write this in standard, or Ax + By = C form, we could begin by multiplying both sides by -5

 

-5y = 8x -15

 

8x + 5y -15 = 0

 

8x + 5y = 15