1) Graph the line that passes through $$ (-3,1) $$ and $$ (5,7) $$. Find the slope of the line that passes through $$ (-3,1) $$ and $$ (5,7) $$. Label this line $$ l_{1} $$.

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To graph the line that passes through the points $$(-3, 1)$$ and $$(5, 7)$$, and to find its slope, 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:

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

Plugging in the given points $$(-3, 1)$$ and $$(5, 7)$$:

$$
m = \frac{7 - 1}{5 - (-3)} = \frac{6}{8} = \frac{3}{4}
$$

**Slope ($$m$$) = $$\frac{3}{4}$$**

### 2. **Determine the Equation of the Line**

Using the point-slope form of the equation of a line:

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

Choose one of the points, say $$(-3, 1)$$, and substitute the values:

$$
y - 1 = \frac{3}{4}(x - (-3)) \
y - 1 = \frac{3}{4}(x + 3) \
$$

Simplify to get the slope-intercept form ($$y = mx + b$$):

$$
y = \frac{3}{4}x + \frac{9}{4} + 1 \
y = \frac{3}{4}x + \frac{13}{4}
$$

**Equation of the line ($$l_1$$):**

$$
y = \frac{3}{4}x + \frac{13}{4}
$$

### 3. **Graphing the Line**

While I can't provide a visual graph here, I can guide you through the steps to graph it manually:

1. **Plot the Points:**
   - Plot the first point at $$(-3, 1)$$.
   - Plot the second point at $$(5, 7)$$.

2. **Draw the Line:**
   - Use a ruler to draw a straight line passing through both points.
   - This line represents $$l_1$$.

3. **Label the Line:**
   - Label the line as $$l_1$$ on your graph.

### **Summary**

- **Points:** $$(-3, 1)$$ and $$(5, 7)$$
- **Slope ($$m$$):** $$\frac{3}{4}$$
- **Equation of $$l_1$$:** $$y = \frac{3}{4}x + \frac{13}{4}$$
- **Graph:** A straight line through the points $$(-3, 1)$$ and $$(5, 7)$$, labeled $$l_1$$.

Feel free to use graphing paper or a graphing tool to visualize the line based on the points and the equation provided.
To graph the line passing through $$(-3,1)$$ and $$(5,7)$$, first find the slope $$m = \frac{3}{4}$$. The equation of the line is $$y = \frac{3}{4}x + \frac{13}{4}$$. Label this line as $$l_1$$.

Graph the line that passes through
and . Find the slope of the line that
passes through and . Label this
line .

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Graph the line that passes through and . Find the slope of the line that passes through and . Label this line .