Comparing Line Slopes: Finding Smaller Angle Between -6 and 1/2 Slopes

Question

Two lines have slopes of $-6$ and $\frac{1}{2}$ .

Which of the lines forms a smaller angle with the x-axis?

00:00 Find which of the lines has a smaller angle with the X-axis

00:03 Use the formula to calculate slope based on angle with X-axis

00:07 Substitute the slope according to given data and calculate the angle

00:11 Isolate the angle

00:18 This is the angle of the first line

00:21 Find the angle of the line relative to X-axis

00:26 This is the angle relative to X-axis

00:31 Use the same method to find the angle of the second line

00:36 Substitute the slope according to given data and calculate the angle

00:40 Isolate the angle

00:45 This is the angle of the second line

00:50 And this is the solution to the question

We will use the formula:

$m=\tan\alpha$

Let's check the slope of minus 6:

$-6=\tan\alpha$

$\tan^{-1}(-6)=\alpha$

$-80.53=\alpha$

$180-80.53=$

$99.47=\alpha_1$

Let's check the slope of one-half:

$\frac{1}{2}=\tan\alpha$

$\tan^{-1}(\frac{1}{2})=\alpha$

$26.56=\alpha_2$

$\alpha_1 > \alpha_2$

The line with a slope of $\frac{1}{2}$