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To find the point-slope form equation for the line that passes through the points \( (15, 10) \) and \( (16, 15) \), we need to follow these steps:

### 1. Find the slope (m):
The formula for slope is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \( (15, 10) \) and \( (16, 15) \):
\[
m = \frac{15 - 10}{16 - 15} = \frac{5}{1} = 5
\]

### 2. Use the point-slope form:
The point-slope form of a line is:

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

Since we are using the first point \( (15, 10) \) and the slope \( m = 5 \), the equation becomes:

\[
y - 10 = 5(x - 15)
\]

This is the point-slope equation for the line that passes through the points \( (15, 10) \) and \( (16, 15) \).

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Would you like more details or have any questions on this? 

Here are five related questions to expand on this concept:
1. How do you convert the point-slope form to slope-intercept form?
2. Can the point-slope form be derived from any two points on a line?
3. What happens if the slope of the line is zero?
4. How do you find the equation of a line perpendicular to the one you just calculated?
5. How would the equation change if we used the second point \( (16, 15) \) instead?

**Tip**: Remember that point-slope form is useful when you have the slope and one point on the line.

Find the point-slope equation for the line that passes through the points (15, 10) and (16, 15). Use the first point in your equation.

Learn how to find the point-slope equation for a line that passes through the points (15, 10) and (16, 15). This problem covers key algebraic concepts such as point-slope form and calculating the slope using two points. Suitable for students in Grades 9-11.

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