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

Question

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

Video Solution

Solution Steps

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 Solution

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

  • Step 1: Calculate the Slope.
    The slope m m of the line can be found using the tangent of the angle. The angle given is 180∘ 180^\circ .
    Therefore, m=tan⁡(180∘)=0 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 y -value.
    The point given is (2,2) (2, 2) , meaning the line's equation is y=2 y = 2 .

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

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

Answer

y=2 y=2

More Questions

Related Subjects

Finding a Linear Equation

Question Types

Equation of a Straight Line: Using the angle formed by the line with the axes