Question

Find an equation for the line that passes through the point P(-5,-3) and is parallel to the line

7x + 4y
10. Use exact values.

Answer 1

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Answer:
`\textsf{y = -1.75x - 11.75}`

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Given:
`\textsf{Goes through (-5, -3) and parallel to 7x + 4y = 10}`

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

Solution: We need to first solve for y in the equation that was provided so we can determine the slope. Then we plug in the values into the point-slope form, distribute, simplify, and solve for y to get our final equation.

Subtract 7x from both sides

• 
  `\textsf{7x - 7x + 4y = 10 - 7x}`

• 
  `\textsf{4y = 10 - 7x}`

Divide both sides by 4

• 
  `\textsf{4y/4 = (10 - 7x)/4}`

• 
  `\textsf{y = (10 - 7x)/4}`

• 
  `\textsf{y = 10/4 - 7x/4}`

• 
  `\textsf{y = 2.5 - 1.75x}`

Plug in the values

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

• 
  `\textsf{y - (-3) = -1.75(x - (-5))}`

Simplify and distribute

• 
  `\textsf{y + 3 = -1.75(x + 5)}`

• 
  `\textsf{y + 3 = (-1.75 * x) + (-1.75 * 5)}`

• 
  `\textsf{y + 3 = -1.75x - 8.75}`

Subtract 3 from both sides

• 
  `\textsf{y + 3 - 3 = -1.75x - 8.75 - 3}`

• 
  `\textsf{y = -1.75x - 8.75 - 3}`

• 
  `\textsf{y = -1.75x - 11.75}`

Therefore, the final equation in slope-intercept form that follows the information that was provided is y = -1.75x - 11.75