What is an equation of the line that passes through the point (-2, -3) and is parallel to the line 5x + 2y = 14?

2y + 5x + 16 = 0

Step-by-step explanation:

To solve this you need to understand the principle/ conditions for parallelism and perpendicularity.

for two lines to be parallel to each other, their gradients or slopes (m) must be equal, that is  m₁ = m₂

Now from the given equation,

5x + 2y = 14 , we need to rearrange it to conform to the equation of a straight line so that the gradient could be established. ie

y = mx + c where m is the gradient

 2y = -5x  + 14

   y = -5x/2  + 14/2

   y = ⁻⁵ˣ/₂  + 7 , therefore , m₁ = ⁻⁵/₂ and m₂ = ⁻⁵/₂ ( parallelism Rule )

The next step is to find the value of C using the coordinate ( -2, -3 )

  -3 = ⁻⁵/₂ ˣ ⁻² + C,

  -3 =  ¹⁰/₂  + C

  -3 =  5 + C

   C = -8.

Now to find the equation of the line that passed through the coordinate

  y = mx + c

  y = ⁻⁵ˣ/₂  - 8

  2y = -5x - 16

  2y + 5x + 16 = 0.

step-by-step explanation: