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To solve the problem of writing the equation of a line using the point-slope form, we start with the formula:

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

where \( (x_1, y_1) \) is a point on the line, and \( m \) is the slope of the line.

From the given problem, the point is \( (-13, 15) \) and the slope \( m = 1 \).

Substituting these values into the point-slope form:

\[
y - 15 = 1(x - (-13))
\]

Simplifying the equation:

\[
y - 15 = 1(x + 13)
\]

To make it even simpler:

\[
y - 15 = x + 13
\]

Now, solve for \( y \) by adding 15 to both sides:

\[
y = x + 13 + 15
\]

\[
y = x + 28
\]

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

\[
y = x + 28
\]

If you'd like further details or have any questions, let me know!

Here are 5 related questions to expand on this topic:
1. How do you convert point-slope form to slope-intercept form?
2. What is the general formula for the point-slope form of a line?
3. Can you use another form of the equation (e.g., standard form) to express this line?
4. How do you interpret the slope of the line geometrically?
5. What would the equation be if the slope were negative instead of positive?

**Tip:** Always double-check your sign when substituting into the point-slope formula, especially if you're dealing with negative coordinates.

Use point-slope form to write the equation of a line that passes through the point (−13, 15) with slope 1.

Learn how to use the point-slope form to find the equation of a line that passes through the point (-13, 15) with slope 1. This algebra problem covers key concepts in linear equations and demonstrates how to transform the equation into slope-intercept form.

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