What is an equation of the line that passes through the point (-5,-5) and is perpendicular to the line 5x-3y=27

Question

this is hard i really need help

Answer 1

Hi Stephanie,

Rewrite the equation in the slope-intercept form: y = mx + b

5x - 3y =27

-3y = -5x +27 

   y = -5x/-3 + 27/-3

y = (5/3)x -9

The slope of this line is m = 5/3. The slope of a line perpendicular to this line is m' = - 3/5. Keep in mind that the product of this slopes must equal minus one ( -1) Check

Keep in mind that the product of this slopes must equal minus one ( -1) 

Check

5/3*-3/5 = -1

So the slope is m' = -3/5, the point through which the line passes is (-5, -5) plug this values in the equation below to find

y = mx +b

-5 =(-3/5)(-5) + b

-5 = 3 +b giving b = -8

y =-3x/5 -8   is the equation of the line perpendicular to the given line passing through (-5, -5).

Answer 2

The Standard Format of the equation of a line looks like:  Ax+By=C

The Slope-Intercept Format of the equation of a line looks like: y=mx+b  [where m=slope and b=y-intercept].

 

Convert Ax+By=C into y=mx+b once and get y=(-A/B)x+(C/B).   Thus, slope=m=(-A/B).

 

The slope of all perpendicular lines is the negative reciprocal of the slope of the line:  (that is, B/A)

 

The perpendicular line is:

      3x + 5y = D      [swap A and B and make negative;  we need point (-5,-5) to find D]

    3(-5) + 5(-5) = D

      -15 -25 = D

          -40 = D

 

The equation of the perpendicular line (in Standard Format) is:    3x + 5y = -40

Answer 3

5x - 3y = 27

-3y = -5x + 27

y = ⁵/₃ x - 9

 

A perpendicular line requires the negative reciprocal of the current slope, so we flip the slope and the sign. That makes the new slope -³/₅.

We can use the point-slope formula to solve this:

y - (-5) = -³/₅(x - (-5))

y + 5 = -³/₅(x + 5)

y + 5 = -³/₅ x - 3

y = -³/₅ x - 8

Answer 4

The keyword is "perpendicular."  The slopes of perpendicular lines are negative reciprocals.

 

First, put the given equation into slope-intercept form, y = mx + b, so you can read the slope.

 

 

5x - 3y = 27

 

-3y = - 5x + 27

 

y = (5/3)x - 9

 

The slope is 5/3.  The slope of the equation you have to build is negative 3/5.

 

Start filling in the slope-intercept equation: y = mx + b

 

y = - (3/5)x + b.

 

Use the point you were given to determine the y-intercept, b.

 

- 5 = -(3/5)(- 5) + b

 

Simplify.

 

- 5 = 3 + b

 

- 8 = b

 

Plug in b and you're done.

 

y = - (3/5)x - 8.

 

 

The SAT always has a problem like this, as well as one where "parallel" is the keyword.  Parallel lines have the same slope.