Find the Equation: Line Parallel to y=4 Passing Through (1,2)

Question

Given the line parallel to the line y=4 y=4

and passes through the point (1,2) (1,2) .

Which of the algebraic representations is the corresponding one for the given line?

Video Solution

Solution Steps

00:00 Find the algebraic representation of the function
00:03 We'll use the linear equation
00:10 The line's slope is 0, parallel lines have identical slopes
00:19 Let's substitute the point according to the given data
00:28 Let's substitute the line's slope according to the given data
00:32 Let's continue solving to find the intersection point
00:35 This is the intersection point with the Y-axis
00:40 Now let's substitute the intersection point and slope in the linear equation
00:51 And this is the solution to the question

Step-by-Step Solution

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

  • Step 1: Identify the key characteristics of the line parallel to y=4 y = 4 .
  • Step 2: Use the point (1,2) (1,2) to determine the new horizontal line equation.
  • Step 3: Write the equation based on the consistent y-value of the line.

Now, let's work through each step:

Step 1: The given line y=4 y = 4 is a horizontal line. All horizontal lines have equations in the form y=c y = c , where c c is a constant value describing the uniform y-position of the line.

Step 2: A line parallel to y=4 y = 4 that also passes through the point (1,2) (1,2) would maintain a constant y-value. Since it must pass through (1,2) (1,2) , its y-intercept is y=2 y = 2 .

Step 3: Therefore, the equation of the line parallel to y=4 y = 4 through (1,2) (1,2) is simply y=2 y = 2 . This ensures it parallels the horizontal direction.

Thus, the algebraic representation of the line parallel to y=4 y=4 and passing through the point (1,2) (1,2) is y=2 y = 2 .

Answer

y=2 y=2