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

Q: Why isn't the equation x = 1 since the point has x-coordinate 1?

Because we need a line parallel to y = 4, which is horizontal! The equation x = 1 would give us a vertical line, not parallel to our horizontal reference line.

Q: How do I know if a line is horizontal or vertical?

Look at the equation format: y = constant means horizontal (like y = 4), while x = constant means vertical (like x = 3). The variable that's NOT constant tells you the direction!

Q: What if the given point was (3,2) instead of (1,2)?

The equation would still be $ y = 2 $! For horizontal lines, only the y-coordinate matters because all points on the line have the same y-value.

Q: Can two horizontal lines ever intersect?

No! Horizontal lines are either the same line (if they have the same y-value) or they're parallel and never meet. That's why $ y = 4 $ and $ y = 2 $ never intersect.

Q: How do I remember which coordinate to use?

Think of it this way: horizontal lines go left and right, so the y-value stays the same while x changes. Use the y-coordinate from your given point for the equation!

Parallel Lines with Horizontal Orientation

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

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

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

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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 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 written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

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

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

Step-by-step solution

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

Step 1: Identify the key characteristics of the line parallel to $y = 4$ .
Step 2: Use the point $(1,2)$ 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 $y = 4$ is a horizontal line. All horizontal lines have equations in the form $y = c$ , where $c$ is a constant value describing the uniform y-position of the line.

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

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

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

Final Answer

$y=2$

Key Points to Remember

Essential concepts to master this topic

Rule: Parallel lines have identical slopes and same direction
Technique: Horizontal line $y = 4$ stays horizontal through $(1,2)$
Check: Point $(1,2)$ satisfies $y = 2$ since 2 = 2 ✓

Common Mistakes

Avoid these frequent errors

Confusing x and y coordinates when writing horizontal line equations
Don't write x = 2 because the point is (1,2) = wrong line direction! This creates a vertical line instead of horizontal. Always use the y-coordinate for horizontal lines: y = 2.

Practice Quiz

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Which statement best describes the graph below?

FAQ

Everything you need to know about this question

Why isn't the equation x = 1 since the point has x-coordinate 1?

Because we need a line parallel to y = 4, which is horizontal! The equation x = 1 would give us a vertical line, not parallel to our horizontal reference line.

How do I know if a line is horizontal or vertical?

Look at the equation format: y = constant means horizontal (like y = 4), while x = constant means vertical (like x = 3). The variable that's NOT constant tells you the direction!

What if the given point was (3,2) instead of (1,2)?

The equation would still be $y = 2$ ! For horizontal lines, only the y-coordinate matters because all points on the line have the same y-value.

Can two horizontal lines ever intersect?

No! Horizontal lines are either the same line (if they have the same y-value) or they're parallel and never meet. That's why $y = 4$ and $y = 2$ never intersect.

How do I remember which coordinate to use?

Think of it this way: horizontal lines go left and right, so the y-value stays the same while x changes. Use the y-coordinate from your given point for the equation!

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