Find the equation of the line that passes through the points (2, 5) and (−3, 6).

Put the equation of the line in the form y  =  mx + b and then enter the values of m and b into the answer box below (in that order), separated with a comma.

To find the equation of the line that passes through two points \((2, 5)\) and \((-3, 6)\), we'll use the slope-intercept form of a line:

\[
y = mx + b
\]

### Step 1: Find the slope \(m\).
The slope formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Substitute the given points \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (-3, 6)\):

\[
m = \frac{6 - 5}{-3 - 2} = \frac{1}{-5} = -\frac{1}{5}
\]

### Step 2: Use the slope to find the y-intercept \(b\).
We now substitute the slope \(m = -\frac{1}{5}\) and one of the points into the equation \(y = mx + b\) to solve for \(b\). Let's use the point \((2, 5)\):

\[
5 = -\frac{1}{5}(2) + b
\]

Simplify and solve for \(b\):

\[
5 = -\frac{2}{5} + b
\]
\[
b = 5 + \frac{2}{5} = \frac{25}{5} + \frac{2}{5} = \frac{27}{5}
\]

### Step 3: Write the equation of the line.
Now that we have \(m = -\frac{1}{5}\) and \(b = \frac{27}{5}\), the equation of the line is:

\[
y = -\frac{1}{5}x + \frac{27}{5}
\]

Thus, the values of \(m\) and \(b\) are:

\[
m = -\frac{1}{5}, \quad b = \frac{27}{5}
\]

The final answer is: 
\[
-1/5, 27/5
\]

Would you like further clarification on any step?

---

Here are 5 follow-up questions:
1. How do you calculate the slope between any two points?
2. Why is the slope negative in this case?
3. What happens if the slope of a line is zero?
4. How does changing the slope affect the steepness of a line?
5. Can a line have the same slope but different intercepts?

**Tip:** Always choose points that are easy to work with when plugging into the slope-intercept formula.

Find the equation of the line that passes through the points (2, 5) and (−3, 6). Put the equation of the line in the form y = mx + b and then enter the values of m and b into the answer box below (in that order), separated with a comma.

Learn how to find the equation of a line that passes through the points (2, 5) and (−3, 6). This problem demonstrates how to calculate the slope and y-intercept using the slope-intercept formula y = mx + b. Suitable for students in Grades 8-10.

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