Find the inclination $\theta$ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $7 x + 5 y = 0$
A) $\Theta \approx 2.2318 \text { radians } \approx 127.9 ^ { \circ }$
B) $\theta \approx 2.2318 \text { radians } \approx 128.9 ^ { \circ }$
C) $\theta \approx 2.2318 \text { radians } \approx 126.9 ^ { \circ }$
D) $\theta \approx 2.2318 \text { radians } \approx 129.9 ^ { \circ }$
E) $\theta \approx 2.2318 \text { radians } \approx 125.9 ^ { \circ }$

Question

Find the inclination $\theta$ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.  $7 x + 5 y = 0$ 
A) $\Theta \approx 2.2318 \text { radians } \approx 127.9 ^ { \circ }$
B) $\theta \approx 2.2318 \text { radians } \approx 128.9 ^ { \circ }$
C) $\theta \approx 2.2318 \text { radians } \approx 126.9 ^ { \circ }$
D) $\theta \approx 2.2318 \text { radians } \approx 129.9 ^ { \circ }$
E) $\theta \approx 2.2318 \text { radians } \approx 125.9 ^ { \circ }$

Quizplus · Accepted Answer

The inclination $\theta$ of a line with the equation $7x + 5y = 0$ can be found by first solving for $y$ in terms of $x$, which gives $y = -\frac{7}{5}x$. The slope $m = -\frac{7}{5}$ represents the tangent of the angle of inclination, so $\theta = \arctan\left(-\frac{7}{5}\right)$. Since the arctan function returns values in the range $(- \frac{\pi}{2}, \frac{\pi}{2})$, and we are dealing with a negative slope, we need to add $\pi$ to the result to get the angle in the correct quadrant, which gives $\theta \approx 2.2318$ radians. Converting to degrees, $\theta \approx 127.9^\circ$.

Find the Inclination θ\thetaθ (In Radians and Degrees) of the Line 7x+5y=07 x + 5 y = 07x+5y=0

Find the Inclination $\theta$ (In Radians and Degrees) of the Line $7 x + 5 y = 0$