Graph the line with slope $$ -\frac{1}{2} $$ passing through the point $$ (-3,3) $$

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1. Start with the point-slope form of a line:
   $$
   y - y_1 = m(x - x_1)
   $$
   Given $$ m = -\frac{1}{2} $$ and the point $$(x_1, y_1) = (-3, 3)$$, substitute into the formula:
   $$
   y - 3 = -\frac{1}{2}\left(x - (-3)\right)
   $$
   
2. Simplify the expression inside the parentheses:
   $$
   y - 3 = -\frac{1}{2}(x + 3)
   $$

3. Distribute the slope on the right-hand side:
   $$
   y - 3 = -\frac{1}{2}x - \frac{3}{2}
   $$

4. Solve for $$ y $$ by adding 3 to both sides:
   $$
   y = -\frac{1}{2}x - \frac{3}{2} + 3
   $$
   Since $$ 3 = \frac{6}{2} $$, combine like terms:
   $$
   y = -\frac{1}{2}x + \frac{3}{2}
   $$

5. The slope-intercept form of the line is:
   $$
   y = -\frac{1}{2}x + \frac{3}{2}
   $$
   This shows a slope of $$-\frac{1}{2}$$ and a $$y$$-intercept at $$\left(0, \frac{3}{2}\right)$$.

6. To graph the line:
   - Plot the point $$(-3, 3)$$ through which the line passes.
   - Plot the $$y$$-intercept $$\left(0, \frac{3}{2}\right)$$.
   - Draw a line through these points, ensuring that for every 2 units moved horizontally, the line moves 1 unit vertically in the opposite direction (decreasing since the slope is negative).

This is the graph of the line with the given slope and point.
To graph the line with a slope of $$-\frac{1}{2}$$ passing through the point $$(-3, 3)$$, follow these steps: 1. **Find the Equation:** - Use the point-slope form: $$ y - y_1 = m(x - x_1) $$. - Substitute $$ m = -\frac{1}{2} $$ and $$(x_1, y_1) = (-3, 3)$$: $$ y - 3 = -\frac{1}{2}(x + 3) $$ - Simplify: $$ y = -\frac{1}{2}x + \frac{3}{2} $$ 2. **Plot Points:** - Plot the given point $$(-3, 3)$$. - Plot the $$y$$-intercept at $$(0, \frac{3}{2})$$. 3. **Draw the Line:** - Use the slope $$-\frac{1}{2}$$ to determine the direction of the line. - For every 2 units moved horizontally, move 1 unit down vertically. - Draw a straight line through the plotted points. This graph represents the line with the specified slope and passing through the given point.

Graph the line with slope passing through the point

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