Write an equation of the line that passes through the given points.(-3,6​) and (1​,2​)

To find the equation of the line passing through the points \((-3, 6)\) and \((1, 2)\), we use the **slope-intercept form** of a line equation:

\[
y = mx + b
\]

### Step 1: Calculate the slope (\(m\))
The slope (\(m\)) is calculated using the formula:

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

Substitute the points \((-3, 6)\) and \((1, 2)\):

\[
m = \frac{2 - 6}{1 - (-3)} = \frac{-4}{1 + 3} = \frac{-4}{4} = -1
\]

### Step 2: Use the slope and a point to find the y-intercept (\(b\))
Substitute the slope \(m = -1\) and one of the points (e.g., \((-3, 6)\)) into the slope-intercept form \(y = mx + b\):

\[
6 = -1(-3) + b
\]

\[
6 = 3 + b
\]

\[
b = 6 - 3 = 3
\]

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

\[
y = -x + 3
\]

### Final Answer:
The equation of the line is:

\[
y = -x + 3
\]

Would you like more details or further clarification? Here are 5 related questions you might find interesting:

1. How can you convert this equation to standard form?
2. What is the perpendicular slope to this line?
3. How do you graph the line given the equation \(y = -x + 3\)?
4. What is the equation of a line parallel to \(y = -x + 3\) passing through a different point?
5. How can you find the distance between this line and a point not on the line?

**Tip:** Always verify your slope and intercept calculations by substituting the points back into the final equation!

Write an equation of the line that passes through the given points (-3, 6) and (1, 2).

Learn how to find the equation of a line passing through the points (-3, 6) and (1, 2) with step-by-step instructions. This solution covers concepts such as slope calculation, slope-intercept form, and linear equations, suitable for Grades 8-10.

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