Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Passing through $$ (-3,6) $$ and $$ (2,1) $$ What is the equation of the line in point-slope form? (Simplify your answer. Use integers or fractions for any numbers in the equation.) What is the equation of the line in slope-intercept form? (Simplify your answer. Use integers or fractions for any numbers in the equation.)

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To find the equation of the line passing through the points $$(-3, 6)$$ and $$(2, 1)$$, we'll follow these steps:

### 1. Calculate the Slope ($$m$$)
The slope of a line passing through two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is given by:

$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

Substituting the given points:

$$
m = \frac{1 - 6}{2 - (-3)} = \frac{-5}{5} = -1
$$

### 2. Point-Slope Form
The point-slope form of a line is:

$$
y - y_1 = m(x - x_1)
$$

Using the point $$(-3, 6)$$ and the slope $$m = -1$$:

$$
y - 6 = -1(x - (-3)) \
y - 6 = -1(x + 3)
$$

**Simplified Point-Slope Form:**

$$
y - 6 = -1(x + 3)
$$

### 3. Slope-Intercept Form
The slope-intercept form of a line is:

$$
y = mx + b
$$

We already have the slope $$m = -1$$. To find $$b$$, the y-intercept, use one of the points. Let's use $$(2, 1)$$:

$$
1 = -1(2) + b \
1 = -2 + b \
b = 3
$$

**Slope-Intercept Form:**

$$
y = -x + 3
$$

### **Final Answers:**

- **Point-Slope Form:** $$ y - 6 = -1(x + 3) $$
- **Slope-Intercept Form:** $$ y = -x + 3 $$
- **Point-Slope Form:** $$ y - 6 = -1(x + 3) $$ - **Slope-Intercept Form:** $$ y = -x + 3 $$

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