Answered

IDNLearn.com provides a comprehensive platform for finding accurate answers. Get accurate and detailed answers to your questions from our dedicated community members who are always ready to help.

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.

Sagot :

Igoroleshko156idn

-------------------------------------------------------------------------------------------------------------

Answer:  [tex]\textsf{y = -1.75x - 11.75}[/tex]

-------------------------------------------------------------------------------------------------------------

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

Find:  [tex]\textsf{The equation in slope-intercept form}[/tex]

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

  • [tex]\textsf{7x - 7x + 4y = 10 - 7x}[/tex]
  • [tex]\textsf{4y = 10 - 7x}[/tex]

Divide both sides by 4

  • [tex]\textsf{4y/4 = (10 - 7x)/4}[/tex]
  • [tex]\textsf{y = (10 - 7x)/4}[/tex]
  • [tex]\textsf{y = 10/4 - 7x/4}[/tex]
  • [tex]\textsf{y = 2.5 - 1.75x}[/tex]

Plug in the values

  • [tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex]
  • [tex]\textsf{y - (-3) = -1.75(x - (-5))}[/tex]

Simplify and distribute

  • [tex]\textsf{y + 3 = -1.75(x + 5)}[/tex]
  • [tex]\textsf{y + 3 = (-1.75 * x) + (-1.75 * 5)}[/tex]
  • [tex]\textsf{y + 3 = -1.75x - 8.75}[/tex]

Subtract 3 from both sides

  • [tex]\textsf{y + 3 - 3 = -1.75x - 8.75 - 3}[/tex]
  • [tex]\textsf{y = -1.75x - 8.75 - 3}[/tex]
  • [tex]\textsf{y = -1.75x - 11.75}[/tex]

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

Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.