Question

Select the correct answer. What is the slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of `3/4`? A. `y = -(3)/(4) x -(1)/(4)` B. `y = 3/4 x +(1)/(4)` C. `y = 3/4 x -(31)/(4)` D. `y = 3/4 x +(31)/(4)`

Answer 1

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Answer:
`\textsf{y = 3/4x - 7.75}`

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Given:
`\textsf{Passes through (5, -4) with a slope of 3/4}`

Find:
`\textsf{The equation in slope-intercept form}`

Solution: In order to determine the equation we need to first plug the values into the point-slope form, simplify, distribute, and solve for y to get our final result.

Plug in the values

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

• 
  `\textsf{y - (-4) = 3/4(x - 5)}`

Simplify the expression and distribute

• 
  `\textsf{y + 4 = 3/4(x - 5)}`

• 
  `\textsf{y + 4 = (3/4 * x) + (3/4 * -5)}`

• 
  `\textsf{y + 4 = 3/4x - 3.75}`

Subtract 4 from both sides

• 
  `\textsf{y + 4 - 4 = 3/4x - 3.75 - 4}`

• 
  `\textsf{y = 3/4x - 3.75 - 4}`

• 
  `\textsf{y = 3/4x - 7.75}`

The equation in slope-intercept form that follows the information that was provided is y = 3/4x - 7.75