through: $$ (-1,5) $$, parallel to $$ y=-5 x+5 $$

Question

UpStudy AI · Accepted Answer

To find the equation of a line that passes through the point $$(-1, 5)$$ and is parallel to the line $$ y = -5x + 5 $$, follow these steps:

### 1. **Determine the Slope of the Given Line**

The given line is in **slope-intercept form**, which is:

$$ y = mx + b $$

where:
- $$ m $$ is the slope
- $$ b $$ is the y-intercept

For the line $$ y = -5x + 5 $$:
- **Slope ($$ m $$)** = $$-5$$

### 2. **Use the Slope for the Parallel Line**

Parallel lines have **identical slopes**. Therefore, the slope of the line we want to find is also $$-5$$.

### 3. **Apply the Point-Slope Formula**

The **point-slope form** of a line equation is:

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

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

Given the point $$(-1, 5)$$ and slope $$ m = -5 $$:

$$ y - 5 = -5(x - (-1)) $$
$$ y - 5 = -5(x + 1) $$

### 4. **Simplify to Slope-Intercept Form (Optional)**

To express the equation in **slope-intercept form** ($$ y = mx + b $$):

$$ y - 5 = -5x - 5 $$
$$ y = -5x - 5 + 5 $$
$$ y = -5x $$

### **Final Equation**

The equation of the line that passes through $$(-1, 5)$$ and is parallel to $$ y = -5x + 5 $$ is:

$$ y = -5x $$

### **Graphical Representation**

To visualize:

1. **Original Line:** $$ y = -5x + 5 $$
2. **Parallel Line:** $$ y = -5x $$
3. **Point on Parallel Line:** $$(-1, 5)$$

Both lines will have the same slope, meaning they descend at the same rate but are shifted vertically relative to each other.
The equation of the line passing through $$(-1, 5)$$ and parallel to $$ y = -5x + 5 $$ is $$ y = -5x $$.

through: \( (-1,5) \), parallel to \( y=-5 x+5 \)

Real Tutor Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Geometry Questions