With slope -2/5 through (5,3)

Question

how do i write this equation in standard form

a. 5x+2y=-25

b. 2x+5y=25

c. 2x+5y=-25

d. 2x-5y=25

Answer 1

 

   Start with the general (master) equation of the line:

 

      y  = mx + b 

 

   (5,3) ---> x=5, y = 3 and slope M=-2/5

 

   3 = (-2/5)(5) + b

 

  3 = -2 + b

 

  b = 5

 

 The equation in slope-intercept form is:  y = (-2/5)x + 5

 

Multiplies everything by 5:  5y = -2x + 25

 

 Adds 2x to both sides, so it moves to the left:  5y + 2x = 25

 

    Commutative property:  2x + 5y = 25  <---- the answer is B !!!

 

------------------------------------------

 

Optionally, you can plug x=5 and y=3 into each of the answer options

and rule out which ones that do not work. For example, option A is

   5(5) + 2(-3) = 25 + -6 = 19 which is NOT -25, so option A is NOT the correct answer.

 

Neither is option C or D. Option B is the only one that works.

Answer 2

Start by using point-slope form:

y-3=(-2/5)(x-5)

Convert to slope-intercept form:

y-3=(-2/5)x+2

y=(-2/5)x+5

Then convert to standard form:

(2/5)x+y=5

2x+5y=25