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VectorFundament120

Lines parallel to each others only occur when two slopes of equations are same. The definition of parallel lines is:

[tex] \large \boxed{m_1 = m_2}[/tex]

We are given the equation of a line which is x = -2. For x = a, the equation forms a verical line and has an undefined slope. These below are basic that you may need to learn when learning about the line graph:

  • y = a —> horizontal line; slope is 0.
  • x = a —> vertical line; slope is undefined.
  • For y = a, any a-values would have same x-values. For example, if we are given y = 2 then any domains or x-values can have the range of 2.
  • For x = a, any a-values would have same y-values or range.

Back to the question. We want to find the equation of a line that is parallel to the line x = -2 and passes through (5,4) point. Recall the definition of parallel line that both slopes of equations must equal. Since x = a for any a-values would give an undefined slope. That means our parallel would be x = b.

Because the line passes through (5,4) - for any a-values from x = a would give out the set of all real numbers for range. Therefore the equation of a line is x = 5.

Answer

  • The equation of a line that is parallel to x = -2 and passes through (5,4) is x = 5.

I hope this helps! If you have any doubts or questions, don't hestitate to ask in comment! Good luck on your assignment and have a great day!

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