Question

Find the equation of the line. A line that is parallel to the graph of 2x + 3y = 5 and contains the point (3 , -1).​

Answer 1

• 
  `\qquad \boxed{\large \sf \blue{y }\: = \: - \: (2x)/(3) \: + \: \red{ 1}}`

`\cal{EXPLANATION:}`

Find the slope of the line that is parallel to 2x + 3y = 5:

• 
  `\boxed{\sf \red{m }\: = \: - \frac{ \green{2}}{ \blue{3}} }`

`\\`

Substitute and calculate:

• 
  `\large { \{ m \: = - (2)/(3) }`
• 
  `\large { \{ m \: = 3 }`
• 
  `\large { \{ y \: = - 1 }`
• 
  `y = mx + b`
• 
  `b \: = \: 1`

`\\`

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Answer 2

• 2x+3y=5
• 3y=-2x+5
• y=-2/3x+5/3

On comparison to y=mx+b

• slope=m=-2/3

Parallel lines have equal slopes

• Slope of parallel line=-2/3
• Point (3,-1)

Equation in point slope form

• y-y1=m(x-x1)
• y+1=-2/3(x-3)
• y+1=-2/3x+6
• y=-2/3x+5