If you have been struggling with questions related to points and lines on a coordinate plane, you might be wondering to which line the point (1, 2) belongs. In this blog post, we will explore the process of determining the line to which this point belongs and provide you with a clear explanation.

Understanding the Equation of a Line

Before we can determine the line to which the point (1, 2) belongs, it’s crucial to have a good understanding of the equation of a line. The equation of a line can be expressed in the slope-intercept form: y = mx + b, where m represents the slope of the line and b represents the y-intercept.

By determining the slope (m) and y-intercept (b) of a line, we can find the equation of that line using the provided coordinates or points on the line.

Determining the Slope

To find the slope of a line passing through two points, we can use the formula: m = (y2 – y1) / (x2 – x1). For our given point (1, 2), we can assume it as (x1, y1) and provide another point on the line to calculate the slope.

Let’s assume we have another point (3, 4) on the line. Substituting the values into our slope formula, we get:

  • m = (4 – 2) / (3 – 1)
  • m = 2 / 2
  • m = 1

Therefore, the slope of the line passing through the points (1, 2) and (3, 4) is 1.

Determining the Y-Intercept

With the slope known, we can now find the y-intercept (b) of the line. To do this, we can substitute the coordinates of one of the points (1, 2) and the calculated slope (1) into the slope-intercept form equation (y = mx + b) and solve for b.

Let’s use the coordinates (1, 2) in the equation:

2 = 1(1) + b

2 = 1 + b

b = 2 – 1

b = 1

Therefore, the y-intercept (b) is 1 for the line passing through the point (1, 2).

The Equation of the Line

Now that we have determined the slope (1) and y-intercept (1), we can write the equation of the line using the slope-intercept form:

y = 1x + 1

Thus, the equation of the line passing through the point (1, 2) is y = x + 1.

In conclusion, the point (1, 2) belongs to the line with the equation y = x + 1. By understanding the equation of a line, calculating the slope, and determining the y-intercept, we can confidently find to which line a given point belongs. This knowledge is essential for solving various mathematical problems involving points and lines on a coordinate plane.

We hope this blog post has provided you with a clear explanation of the process to determine the line to which the point (1, 2) belongs. If you have any further questions or need additional assistance, feel free to reach out to us. Happy learning!

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