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The line x + y + 4 = 0 makes an angle of \(\theta\) with the...

Further Mathematics
WAEC 2024

The line x + y + 4 = 0 makes an angle of \(\theta\) with the x-axis. Find the value of \(\theta\)

  • A. 315\(^0\)
  • B. 225\(^0\)
  • C. 135\(^0\)
  • D. 45\(^0\)
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Correct Answer: Option A
Explanation

The line x + y + 4 = 0

y = - x - 4 (in the slope-intercept form)

m = -1

But, Tan \(\theta\) = - 1 = slope/gradient

\(\theta\) = tan\(^{-1}\)(-1) = - 45º

But, tan -45º is in the fourth quadrant, since the line made an angle with the x-axis, the positive value = 360 - 45 = 315\(^0\)


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