Linear Equation: Find Line Through Point (2,2) at 180 Degrees

Q: What does 180° with the positive x-axis actually mean?

It means the line points in the opposite direction from the positive x-axis. Think of it like an arrow pointing left instead of right, but the line itself is still horizontal.

Q: Why isn't the slope -1 or some negative number?

The angle tells us the direction, not necessarily a negative slope! At 180°, we're pointing left but still horizontally, so $ \tan(180°) = 0 $.

Q: How do I write the equation of a horizontal line?

A horizontal line has the form $ y = k $ where k is a constant. Since it passes through (2,2), we get y = 2.

Q: How can I verify this is correct?

Check that the point (2,2) satisfies $ y = 2 $: substitute to get 2 = 2 ✓. Also verify the line is horizontal by confirming the slope is zero.

Horizontal Lines with Angle Measurement

Choose the equation that represents a straight line that passes through the point $(2,2)$ and creates an angle of 180 degrees with the positive part of the x axis.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the algebraic representation of the function

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

00:07 Substitute the given angle and calculate to find the slope

00:11 This is the line's slope

00:15 Now let's use the line equation

00:20 Substitute the point according to the given data

00:27 Substitute the slope and solve to find the intersection point (B)

00:35 This is the intersection point with the Y-axis

00:41 Now substitute the intersection point and slope in the line equation

00:55 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

Choose the equation that represents a straight line that passes through the point $(2,2)$ and creates an angle of 180 degrees with the positive part of the x axis.

Step-by-step solution

To solve this problem, we'll find the equation of a line passing through $(2,2)$ that makes an angle of $180^\circ$ with the positive x-axis.

Step 1: Calculate the Slope.
The slope $m$ of the line can be found using the tangent of the angle. The angle given is $180^\circ$ .
Therefore, $m = \tan(180^\circ) = 0$ .
This tells us that the line is horizontal.
Step 2: Apply the Point-Slope Form.
Since the line is horizontal (slope = 0), it has a constant $y$ -value.
The point given is $(2, 2)$ , meaning the line's equation is $y = 2$ .

Thus, the equation of the line is $y = 2$ . This corresponds to choice $4$ in the given options, confirming that it meets all criteria of the problem.

Therefore, the solution to the problem is $y = 2$ .

Final Answer

$y=2$

Key Points to Remember

Essential concepts to master this topic

Angle Rule: 180° with positive x-axis means horizontal line
Technique: Calculate slope using m = tan(180°) = 0
Check: Horizontal line through (2,2) must have equation y = 2 ✓

Common Mistakes

Avoid these frequent errors

Using angle to find non-zero slope
Don't calculate tan(180°) as undefined or non-zero = wrong slope! 180° means the line points in the negative x-direction but is still horizontal. Always remember tan(180°) = 0, giving a horizontal line.

Practice Quiz

Test your knowledge with interactive questions

Look at the linear function represented in the diagram.

When is the function positive?

FAQ

Everything you need to know about this question

What does 180° with the positive x-axis actually mean?

It means the line points in the opposite direction from the positive x-axis. Think of it like an arrow pointing left instead of right, but the line itself is still horizontal.

Why isn't the slope -1 or some negative number?

The angle tells us the direction, not necessarily a negative slope! At 180°, we're pointing left but still horizontally, so $\tan(180°) = 0$ .

How do I write the equation of a horizontal line?

A horizontal line has the form $y = k$ where k is a constant. Since it passes through (2,2), we get y = 2.

What if the angle was 0° instead of 180°?

At 0°, you'd still get a horizontal line! Both 0° and 180° give $\tan = 0$ , so both create horizontal lines through the given point.

How can I verify this is correct?

Check that the point (2,2) satisfies $y = 2$ : substitute to get 2 = 2 ✓. Also verify the line is horizontal by confirming the slope is zero.

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