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To find the equation of a line with a given slope and a point, 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, and \( (x_1, y_1) \) is the given point.

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

Substituting these values into the point-slope formula:

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

Simplify the equation:

\[
y - 5 = x - 6
\]

Now, solve for \( y \) to put it into slope-intercept form \( y = mx + b \):

\[
y = x - 6 + 5
\]

\[
y = x - 1
\]

So, the equation of the line in slope-intercept form is:

\[
\boxed{y = x - 1}
\]

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How would the equation change if the slope was different, say \( m = 2 \)?
2. What is the y-intercept of the line you just found?
3. How can you find the x-intercept of the line \( y = x - 1 \)?
4. How would the equation change if the given point was different, such as \( (2, 3) \)?
5. How do you convert the equation \( y = x - 1 \) into standard form?

**Tip:** Remember, the slope-intercept form \( y = mx + b \) is useful for quickly identifying the slope and y-intercept of a line!

Find an equation of the line having a slope of 1 and passing through the point (6, 5). Write the answer in slope-intercept form y = mx + b.

Learn how to find the equation of a line with a slope of 1 passing through the point (6, 5) using the slope-intercept form y = mx + b. This problem is ideal for students in Grades 7-9 and covers key algebraic concepts.

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