Question
What is an equation of the line that passes through the point and is parallel to the line
?

Question

Question What is an equation of the line that passes through the point $$ (-8,-1) $$ and is parallel to the line $$ x-2 y=18 $$ ?

UpStudy AI · Accepted Answer

To find the equation of the line that passes through the point $$ (-8, -1) $$ and is parallel to the line given by the equation $$ x - 2y = 18 $$, we can follow these steps:

1. **Find the slope of the given line**: 
   We need to rewrite the equation $$ x - 2y = 18 $$ in slope-intercept form $$ y = mx + b $$, where $$ m $$ is the slope.

2. **Use the point-slope form**: 
   Once we have the slope, we can use the point-slope form of the equation of a line, which is given by $$ y - y_1 = m(x - x_1) $$, where $$ (x_1, y_1) $$ is the point through which the line passes.

Let's start by finding the slope of the given line.

Rearranging $$ x - 2y = 18 $$ to solve for $$ y $$:

$$
-2y = -x + 18
$$
$$
y = \frac{1}{2}x - 9
$$

From this, we can see that the slope $$ m $$ of the given line is $$ \frac{1}{2} $$.

Since parallel lines have the same slope, the slope of the line we are looking for is also $$ \frac{1}{2} $$.

Now, we can use the point-slope form with the point $$ (-8, -1) $$:

$$
y - (-1) = \frac{1}{2}(x - (-8))
$$

This simplifies to:

$$
y + 1 = \frac{1}{2}(x + 8)
$$

Now, let's simplify this equation to get it into slope-intercept form:

$$
y + 1 = \frac{1}{2}x + 4
$$
$$
y = \frac{1}{2}x + 4 - 1
$$
$$
y = \frac{1}{2}x + 3
$$

Thus, the equation of the line that passes through the point $$ (-8, -1) $$ and is parallel to the line $$ x - 2y = 18 $$ is:

$$
y = \frac{1}{2}x + 3
$$
The equation of the line is $$ y = \frac{1}{2}x + 3 $$.

Question
What is an equation of the line that passes through the point and is parallel to the line
?

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Question What is an equation of the line that passes through the point and is parallel to the line ?

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Question
What is an equation of the line that passes through the point and is parallel to the line
?