17) through: $$ (4,-1) $$, slope $$ =\frac{3}{4} $$

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UpStudy AI · Accepted Answer

To find the equation of a line that passes through the point $$(4, -1)$$ with a slope of $$\frac{3}{4}$$, you can use the **point-slope form** of a linear equation. The point-slope form is given by:

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

where:
- $$m$$ is the slope of the line.
- $$(x_1, y_1)$$ is a point on the line.

**Step-by-Step Solution:**

1. **Identify the given values:**
   - **Point $$(x_1, y_1)$$:** $$(4, -1)$$
   - **Slope $$m$$:** $$\frac{3}{4}$$

2. **Plug the values into the point-slope form:**
   $$
   y - (-1) = \frac{3}{4}(x - 4)
   $$
   
3. **Simplify the equation:**
   $$
   y + 1 = \frac{3}{4}(x - 4)
   $$
   
4. **Distribute the slope on the right-hand side:**
   $$
   y + 1 = \frac{3}{4}x - 3
   $$
   
5. **Isolate $$y$$ to write the equation in slope-intercept form ($$y = mx + b$$):**
   $$
   y = \frac{3}{4}x - 3 - 1
   $$
   $$
   y = \frac{3}{4}x - 4
   $$

**Final Answer:**
$$
y = \frac{3}{4}x - 4
$$
The equation of the line is $$ y = \frac{3}{4}x - 4 $$.

through: , slope

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