+489 The graph of
\(r = \frac{7}{3 \cos \theta + 2 \sin \theta}\)
is a line. Find the slope of this line.
+129918 r = √ [ x^2 + y^2 ]
cos theta = x/r = x / √ [ x^2 + y^2 ]
sin theta = y/r = y / √ [ x^2 + y^2 ]
So we have
√ [ x^2 + y^2 ] = 7
_____________
[ 3x + 2y ]
___________
√ [ x^2 + y^2 ]
√ [ x^2 + y^2 ] = 7 √ [ x^2 + y^2 ]
_____________
3x + 2y
1 = 7
_______
3x + 2y
3x + 2y = 7
In the form Ax + By = C.....the slope is -A / B
So.....slope = -3/2
+26393 The graph of
\(\huge{r = \dfrac{7}{3 \cos \theta + 2 \sin \theta}}\)
is a line. Find the slope of this line.
\(\begin{array}{|rcll|} \hline \mathbf{r(\theta)} &\mathbf{=}& \mathbf{\dfrac{7}{3 \cos \theta + 2 \sin \theta}} \\ \hline r(0) &=& \dfrac{7}{3 \cos(0) + 2 \sin(0)} \\\\ r(0) &=& \dfrac{7}{3} \\ \hline r(90) &=& \dfrac{7}{3 \cos(90) + 2 \sin(90)} \\\\ r(90) &=& \dfrac{7}{2} \\ \hline -m &=& \dfrac{r(90)}{r(0)} \\\\ &=& \dfrac{\dfrac{7}{2}}{ \dfrac{7}{3}} \\\\ -m &=& \dfrac{3}{2} \\\\ \mathbf{m} & \mathbf{=} & \mathbf{-\dfrac{3}{2}} \\ \hline \end{array}\)
