) through: $$ (0,-5) $$, slope $$ =-\frac{2}{5} $$

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UpStudy AI · Accepted Answer

It looks like you're looking to find the equation of a line that passes through the point $$(0, -5)$$ with a slope of $$-\frac{2}{5}$$. Let's derive the equation step by step.

### Given:
- **Point:** $$(0, -5)$$
- **Slope (m):** $$-\frac{2}{5}$$

### Using the Point-Slope Form:
The point-slope form of a line is:
$$
y - y_1 = m(x - x_1)
$$
Where $$(x_1, y_1)$$ is the given point and $$m$$ is the slope.

### Plugging in the Values:
$$
y - (-5) = -\frac{2}{5}(x - 0)
$$
$$
y + 5 = -\frac{2}{5}x
$$

### Solving for $$y$$ to Get the Slope-Intercept Form:
$$
y = -\frac{2}{5}x - 5
$$

### Final Equation:
$$
y = -\frac{2}{5}x - 5
$$

### Alternative Forms:
1. **Standard Form:** Multiply both sides by 5 to eliminate the fraction:
   $$
   5y = -2x - 25
   $$
   Rearranged:
   $$
   2x + 5y = -25
   $$

2. **Intercepts:**
   - **Y-intercept:** $$(0, -5)$$ (already given)
   - **X-intercept:** Set $$y = 0$$ and solve for $$x$$:
     $$
     0 = -\frac{2}{5}x - 5 \implies \frac{2}{5}x = -5 \implies x = -5 \times \frac{5}{2} = -\frac{25}{2}
     $$
     So, the x-intercept is $$\left(-\frac{25}{2}, 0\right)$$.

### Graphical Representation:
The line will cross the y-axis at $$(0, -5)$$ and slope downward to the right, reflecting the negative slope of $$-\frac{2}{5}$$.

If you have any further questions or need additional assistance, feel free to ask!
The equation of the line is $$ y = -\frac{2}{5}x - 5 $$.

) through: , slope

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