Question

What is the equation of the line that passes through the point (5,-2) and has a
slope of -2/5

Answer 1

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Answer:
`\textsf{y = -2/5x}`

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Given:
`\textsf{Passes through (5, -2) and slope of -2/5}`

Find:
`\textsf{The equation that follows the details provided}`

Solution: We first need to plug into the point-slope form and after simplifying, distributing, and solving for y we will complete our equation.

Plug in the values

• 
  `\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}`

• 
  `\textsf{y - (-2) = -2/5(x - 5)}`

Distribute and simplify

• 
  `\textsf{y + 2 = -2/5(x - 5)}`

• 
  `\textsf{y + 2 = (-2/5 * x) + (-2/5 * (-5))}`

• 
  `\textsf{y + 2 = -2/5x + 2}`

Subtract 2 from both sides

• 
  `\textsf{y + 2 - 2 = -2/5x + 2 - 2}`

• 
  `\textsf{y = -2/5x + 2 - 2}`

• 
  `\textsf{y = -2/5x}`

Therefore, the final equation that follows the information that was provided is y = -2/5x.