Write the equation of a line perpendicular to 6x-5y=-8 that passes through the point ​(​-6,2​).

Answer 1

Hi Jordin,

Question: Write the equation of a line perpendicular to 6x-5y=-8 that passes through the point ​(​-6,2​).

The question gives you:

1. the equation of a line 6x-5y = -8
2. a point (-6, 2)

You are to find:

1. a line perpendicular to the given line that passes through the point.

Things we can conclude and formulas we can use

1. the slope of a line perpendicular to another is the negative inverse
2. y = mx + b equation of a line where m is the slope and b is the y intercept
3. (y-y1) = m(x-x1) point slope equation of a line. m = slope, (x1, y1) is a point

1) Determine the slope of the original line

2) Use the point-slope formula to determine the equation of the new line that is perpendicular to the first.

Determine slope of origional line

1) put the equation into the form of y=mx+b where m is the slope

6x-5y = -8

-5y = -6x - 8

y = = 6/5 x + 8/5

The slope is 6/5

The slope of the perpendicular line is the negative inverse of 6/5 so it is -5/6

Use the point slope formula to determine the equation of the line

(y-y1) = m (x-x1) (x1,y1) is the point we want the line to pass through (-6, 2)

(y- 2) = (-5/6)(x-(-6))

y = -5/6 x - 5 + 2

y = -5/6 x -3

The equation of the line that is perpendicular to 6x-5y=-8 that passes through the point ​(​-6,2​) is

y = -5/6 x - 3

Let me know if you need more help or would like to schedule a tutoring session :)