SOLUTION: Resubmission: Find the acute angle that is formed by the line {{{ y-sqrt(3x) +1 = 0 }}} and the x-axis. It says to graph the line and find the slope first?

Algebra ->  Trigonometry-basics -> SOLUTION: Resubmission: Find the acute angle that is formed by the line {{{ y-sqrt(3x) +1 = 0 }}} and the x-axis. It says to graph the line and find the slope first?      Log On


   



Question 1005706: Resubmission:
Find the acute angle that is formed by the line +y-sqrt%283x%29+%2B1+=+0+ and the x-axis.
It says to graph the line and find the slope first?

Found 2 solutions by rothauserc, Alan3354:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
y = sqrt(3x) - 1
y = 3^(1/2) * x^(1/2) - 1
we know point (0, -1) is on the curve - substitute for x in the equation to get the corresponding y coordinate
this curve is a parabola NOT a line
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here is the graph of the parabola
graph%28300%2C+200%2C+-2%2C+10%2C+-10%2C+10%2C+sqrt%283x%29-1%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the acute angle that is formed by the line +y-sqrt%283x%29+%2B1+=+0+ and the x-axis.
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+y-sqrt%283x%29+%2B1+=+0+
That's not a line, it's a curve.
You can find the slope of the line tangent to the curve at y = 0:
---
+y-sqrt%283x%29+%2B1+=+0+
Find the x-intercept:
+y+=+sqrt%283x%29+-1+=+0+
sqrt%283x%29+=+1
3x = 1
x = 1/3
----------------
y' = %281%2F2%29%2A3%2Fsqrt%283x%29
@ x = 1/3:
y' = (3/2)
--
The slope 3/2 is the tangent of the angle.
--> angle =~ 56.31 degs