
Contains (5, 1) and is perpendicular to y = 3. write in standard form


To find the equation of a line that contains the point \((5, 1)\) and is perpendicular to the line \(y = 3\) in standard form, we need to follow these steps:

1. **Determine the slope of the given line**: The given equation is \(y = 3\). This is a horizontal line with a slope \(m = 0\).

2. **Find the slope of the perpendicular line**: The slope of a line perpendicular to a horizontal line (slope 0) is undefined, meaning the line is vertical.

3. **Write the equation of the vertical line**: The equation of a vertical line passing through the point \((5, 1)\) is \(x = 5\).

4. **Express in standard form**: Standard form of a linear equation is \(Ax + By = C\). For a vertical line, the equation \(x = 5\) is already in a form that can be interpreted as standard form with \(A = 1\), \(B = 0\), and \(C = 5\).

So, the standard form of the equation of the line is:
\[ x = 5 \]

Would you like more details or have any questions about this process?

Here are some related questions for further practice:
1. Write the standard form of a line perpendicular to \(y = 2x + 3\) and passing through the point \((4, -1)\).
2. Find the standard form of a line parallel to \(y = -5x + 6\) and passing through \((2, 3)\).
3. Determine the standard form of the line that passes through the points \((1, 2)\) and \((3, 4)\).
4. Write the standard form of a line with slope \(4\) and passing through the point \((0, -2)\).
5. What is the standard form of a line with slope \(-\frac{1}{3}\) passing through the point \((6, 5)\)?
6. Find the standard form of the line perpendicular to \(y = -7x + 1\) passing through the point \((2, 2)\).
7. Determine the standard form of a line with an undefined slope passing through \((2, -3)\).
8. Write the standard form of the horizontal line passing through the point \((4, 2)\).

**Tip:** When converting to standard form, make sure that the coefficients \(A\), \(B\), and \(C\) are integers and that \(A\) is positive.

Learn how to find the equation of a line perpendicular to y = 3 that passes through the point (5, 1). This problem involves concepts of geometry and linear equations, suitable for students in Grades 9-12.

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