Write a linear equation such that the point (1,2) lies on its graph

To write a linear equation where the point \((1, 2)\) lies on its graph, we need to ensure that when \(x = 1\), \(y = 2\). The general form of a linear equation is:

\[
y = mx + b
\]

Where:
- \(m\) is the slope of the line
- \(b\) is the y-intercept

We'll start by using the point \((1, 2)\). Let's arbitrarily choose a slope, say \(m = 3\). Now we substitute the point into the equation to find the y-intercept:

\[
2 = 3(1) + b
\]
\[
2 = 3 + b
\]
\[
b = 2 - 3 = -1
\]

So, the equation of the line is:

\[
y = 3x - 1
\]

This is one possible equation where the point \((1, 2)\) lies on the line. 

Would you like more details on how to choose different slopes or other forms of linear equations?

Here are 5 follow-up questions for deeper understanding:
1. How would the equation change if the slope was \( -2 \)?
2. What is the significance of the slope in the equation of a line?
3. Can you find the equation of a line passing through \((1, 2)\) and \((3, 4)\)?
4. How do you find the slope if you're given two points on a line?
5. What happens to the equation if we change the y-intercept?

**Tip**: To check if a point lies on a line, substitute the coordinates into the equation and see if both sides are equal.

Write a linear equation such that the point (1,2) lies on its graph.

Learn how to write a linear equation where the point (1, 2) lies on its graph. This problem uses the slope-intercept form (y = mx + b) and provides a detailed step-by-step solution, ideal for students in Grades 8-10.

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