Question

What is the equation of the line that passes through the point (4,-8) and has a slope of -3/4

Answer 1

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Answer:
`\textsf{y = -3/4x - 5}`

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Given:
`\textsf{Slope = -3/4 and passes through (4, -8)}`

Find:
`\textsf{Determine the equation of the line that fits the criteria}`

Solution: The first thing that we need to do is plug the information that was provided into the point-slope formula, distribute, and solve for y.

Plug in the values

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

• 
  `\textsf{y - (-8) = -3/4(x - 4)}`

Distribute and simplify

• 
  `\textsf{y + 8 = (-3/4 * x) + (-3/4 * -4)}`

• 
  `\textsf{y + 8 = -3/4x + (-3 * -4)/4}`

• 
  `\textsf{y + 8 = -3/4x + (12)/4}`

• 
  `\textsf{y + 8 = -3/4x + 3}`

Solve for y

• 
  `\textsf{y + 8 - 8 = -3/4x + 3 - 8}`

• 
  `\textsf{y = -3/4x + 3 - 8}`

• 
  `\textsf{y = -3/4x - 5}`

Therefore, the final equation of the line that passes through the point (4, -8) and has a slope of -3/4 is
`\textsf{y = -3/4x - 5}`