Find the equation of the line with slope 1 that contains  the point (5,6)

To find the equation of the line with a slope of \( 1 \) that passes through the point \( (5, 6) \), we can use the **point-slope form** of the equation of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

Where:
- \( m \) is the slope,
- \( (x_1, y_1) \) is a point on the line.

Given:
- Slope \( m = 1 \),
- Point \( (x_1, y_1) = (5, 6) \).

Substitute these values into the point-slope form:

\[
y - 6 = 1(x - 5)
\]

Simplify the equation:

\[
y - 6 = x - 5
\]

Add 6 to both sides:

\[
y = x + 1
\]

Thus, the equation of the line is:

\[
y = x + 1
\]

Would you like to explore more details about this problem or ask further questions?

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Here are 5 related questions:
1. How do you derive the slope-intercept form from the point-slope form?
2. What if the slope was \( -1 \) instead of \( 1 \)? How would the equation change?
3. Can you find the equation of a line perpendicular to this line through the same point?
4. How do we determine if two lines are parallel or perpendicular?
5. How do you graph a line using its equation?

**Tip:** The slope \( m \) represents the steepness of the line. When \( m = 1 \), it means the line rises by 1 unit for every 1 unit it moves to the right.

Find the equation of the line with slope 1 that contains the point (5,6)

Learn how to find the equation of a line with slope 1 passing through the point (5,6). This tutorial explains how to use the point-slope form and convert it into slope-intercept form with a detailed step-by-step guide. Ideal for students in Grades 8-10.

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