Dhe line parallel to $$ 3 x+y=8 $$ that passes through $$ (0,-4) $$

Question

UpStudy AI · Accepted Answer

To find the equation of a line parallel to $$ 3x + y = 8 $$ that passes through the point $$ (0, -4) $$, follow these steps:

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

First, let's find the slope of the line $$ 3x + y = 8 $$.

- **Rearrange the equation to slope-intercept form ($$ y = mx + b $$):**

$$
  y = -3x + 8
  $$

- **Identify the slope ($$ m $$):**

The coefficient of $$ x $$ is the slope. So, $$ m = -3 $$.

### 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 $$ -3 $$.

### 3. Apply the Point-Slope Form

We know the slope $$ m = -3 $$ and a point through which the line passes $$ (0, -4) $$. Since the point is $$ (0, -4) $$, it means the line crosses the y-axis at $$ y = -4 $$. This directly gives us the **y-intercept** ($$ b $$).

So, the equation in slope-intercept form ($$ y = mx + b $$) is:

$$
y = -3x - 4
$$

### 4. Final Answer

The equation of the line parallel to $$ 3x + y = 8 $$ that passes through $$ (0, -4) $$ is:

$$
\boxed{y = -3\,x\;-\;4}
$$
The equation of the line parallel to $$ 3x + y = 8 $$ that passes through $$ (0, -4) $$ is $$ y = -3x - 4 $$.

Dhe line parallel to that passes
through

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Algebra Questions

Dhe line parallel to that passes through