The equation of line

u

is

y

–

3

=

7

(

x

–

5

)

.

Parallel to line

u

is line

v

,

which passes through the point

(

–

1

,

–

9

)

.

What is the equation of line

v

?

*Write* *the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or* *integers.*

We are given the equation of line \( u \) in point-slope form as:

\[
y - 3 = 7(x - 5)
\]

### Step 1: Convert the equation of line \( u \) to slope-intercept form

To do this, we'll expand the equation:

\[
y - 3 = 7(x - 5)
\]

Distribute the 7 on the right side:

\[
y - 3 = 7x - 35
\]

Now, add 3 to both sides to isolate \( y \):

\[
y = 7x - 35 + 3
\]

\[
y = 7x - 32
\]

Thus, the equation of line \( u \) is:

\[
y = 7x - 32
\]

### Step 2: Identify the slope of line \( u \)

From the equation \( y = 7x - 32 \), we see that the slope of line \( u \) is \( m = 7 \).

### Step 3: Determine the equation of line \( v \)

Since line \( v \) is parallel to line \( u \), it will have the same slope, \( m = 7 \).

We are also told that line \( v \) passes through the point \( (-1, -9) \). Now, we can use the point-slope form to write the equation of line \( v \):

\[
y - y_1 = m(x - x_1)
\]

Substitute \( m = 7 \), \( x_1 = -1 \), and \( y_1 = -9 \):

\[
y - (-9) = 7(x - (-1))
\]

Simplify:

\[
y + 9 = 7(x + 1)
\]

### Step 4: Convert to slope-intercept form

Expand the equation:

\[
y + 9 = 7x + 7
\]

Subtract 9 from both sides:

\[
y = 7x + 7 - 9
\]

\[
y = 7x - 2
\]

### Final Answer:
The equation of line \( v \) in slope-intercept form is:

\[
y = 7x - 2
\]

---

Would you like more details or have any questions?

Here are some related questions for further practice:
1. What is the equation of a line perpendicular to \( u \) passing through the point \( (-1, -9) \)?
2. What is the equation of a line parallel to \( u \) passing through \( (2, 3) \)?
3. How do you find the distance between two parallel lines?
4. What is the slope of a line perpendicular to line \( v \)?
5. How would you graph the equation of line \( v \)?

**Tip**: When two lines are parallel, they always have the same slope!

The equation of line u is y – 3 = 7(x – 5). Parallel to line u is line v, which passes through the point (-1, -9). What is the equation of line v? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Learn how to find the equation of a line parallel to y - 3 = 7(x - 5) that passes through the point (-1, -9). This problem covers key algebraic concepts like point-slope and slope-intercept forms, and parallel line properties. Suitable for students in Grades 9-10.

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