Calculate Slope from 100-Degree Angle: Line Direction Analysis

Q: Why is the slope negative when the angle is 100 degrees?

An angle of 100 degrees is in the second quadrant where tangent values are negative. Think of it this way: the line points up and to the left, so as you move right, the line goes down!

Q: How do I know if a line is ascending or descending?

Positive slope = ascending (goes up from left to right)Negative slope = descending (goes down from left to right)Since our slope is -5.67, the line is descending.

Q: What if I don't have a calculator for tan(100°)?

You can use the identity: $ \tan(100°) = \tan(180° - 80°) = -\tan(80°) $. Or remember that $ \tan(100°) = \tan(100° - 180°) = \tan(-80°) $.

Q: Why can't the slope be positive 5.67?

Because 100° is in the second quadrant where x is negative and y is positive. This makes the slope $ \frac{\text{rise}}{\text{run}} = \frac{(+)}{(-)} = (-) $ negative!

Q: Is -5.67 the exact answer?

No, -5.67 is rounded. The exact value is $ \tan(100°) $, but for practical purposes, -5.67 is accurate enough for most problems.

Slope Calculation with Obtuse Angles

Find the slope of a line that makes an angle of 100 degrees with the positive part of the xaxis, and indicate whether the line is ascending or descending.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the slope of the line according to the angle, and indicate if it's increasing or decreasing

00:03 We'll use the formula to calculate the slope according to the angle with the X-axis

00:06 We'll substitute the angle according to the given data and calculate to find the slope

00:15 This is the slope of the line

00:18 If the slope is negative, it means the line is decreasing

00:25 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the slope of a line that makes an angle of 100 degrees with the positive part of the xaxis, and indicate whether the line is ascending or descending.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Use the formula $m = \tan(\theta)$
Step 2: Calculate $\tan(100^\circ)$
Step 3: Determine if the line is ascending or descending based on the slope

Now, let's work through each step:

Step 1: We use the formula for the slope of a line:
$\displaystyle m = \tan(\theta)$

Step 2: Substitute $\theta = 100^\circ$ into the formula:
$\displaystyle m = \tan(100^\circ)$

Using a calculator, $\tan(100^\circ) \approx -5.67$ .

Step 3: Since the slope is negative, the line is descending.

Therefore, the solution to the problem is: $m = -5.67$ , decreasing.

Final Answer

$m=-5.67$ decreasing

Key Points to Remember

Essential concepts to master this topic

Formula: Slope equals tangent of the angle with x-axis
Technique: $m = \tan(100°) = -5.67$ using calculator
Check: Negative slope confirms line descends from left to right ✓

Common Mistakes

Avoid these frequent errors

Using degrees instead of checking calculator mode
Don't assume your calculator is in degree mode = wrong tangent value! Many calculators default to radians, giving tan(100) ≈ -0.587 instead of -5.67. Always verify your calculator is set to degrees before calculating trigonometric functions.

Practice Quiz

Test your knowledge with interactive questions

Look at the function shown in the figure.

When is the function positive?

FAQ

Everything you need to know about this question

Why is the slope negative when the angle is 100 degrees?

An angle of 100 degrees is in the second quadrant where tangent values are negative. Think of it this way: the line points up and to the left, so as you move right, the line goes down!

How do I know if a line is ascending or descending?

Positive slope = ascending (goes up from left to right)
Negative slope = descending (goes down from left to right)
Since our slope is -5.67, the line is descending.

What if I don't have a calculator for tan(100°)?

You can use the identity: $\tan(100°) = \tan(180° - 80°) = -\tan(80°)$ . Or remember that $\tan(100°) = \tan(100° - 180°) = \tan(-80°)$ .

Why can't the slope be positive 5.67?

Because 100° is in the second quadrant where x is negative and y is positive. This makes the slope $\frac{\text{rise}}{\text{run}} = \frac{(+)}{(-)} = (-)$ negative!

Is -5.67 the exact answer?

No, -5.67 is rounded. The exact value is $\tan(100°)$ , but for practical purposes, -5.67 is accurate enough for most problems.

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