The equation of line 

p

 is 

y

=

1

7

x

–

10

.

 Line 

q

,

 which is parallel to line 

p

,

 includes the point 

(

2

,

–

1

)

.

 What is the equation of line 

q

?

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

y

=

Submit




We are given two lines, \( p \) and \( q \), where line \( q \) is parallel to line \( p \). We know the following about line \( p \):

\[
y = \frac{1}{7}x - 10
\]

Since line \( q \) is parallel to line \( p \), the slope of line \( q \) is the same as the slope of line \( p \). The slope of line \( p \) is \( \frac{1}{7} \).

Now, line \( q \) passes through the point \( (2, -1) \). To find the equation of line \( q \), we will use the point-slope form of a line, which is:

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

where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line. In this case, \( m = \frac{1}{7} \), \( x_1 = 2 \), and \( y_1 = -1 \).

Substituting these values into the point-slope form:

\[
y - (-1) = \frac{1}{7}(x - 2)
\]

Simplify the equation:

\[
y + 1 = \frac{1}{7}(x - 2)
\]

Distribute the \( \frac{1}{7} \):

\[
y + 1 = \frac{1}{7}x - \frac{2}{7}
\]

Now, subtract 1 from both sides to get the equation in slope-intercept form \( y = mx + b \):

\[
y = \frac{1}{7}x - \frac{2}{7} - 1
\]

Convert \( 1 \) to a fraction with a denominator of 7:

\[
y = \frac{1}{7}x - \frac{2}{7} - \frac{7}{7}
\]

Simplify:

\[
y = \frac{1}{7}x - \frac{9}{7}
\]

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

\[
y = \frac{1}{7}x - \frac{9}{7}
\]

Let me know if you would like further details or have any questions!

Here are 5 related questions:
1. How do you find the slope of a line from its equation?
2. What is the point-slope form of a line, and when is it useful?
3. How do you determine if two lines are parallel?
4. How can you convert a line's equation from point-slope form to slope-intercept form?
5. How would the equation change if line \( q \) passed through a different point?

**Tip:** Parallel lines always have the same slope but different y-intercepts unless they are identical lines.

The equation of line p is y = 1/7x - 10. Line q, which is parallel to line p, includes the point (2, -1). What is the equation of line q? Write the equation in slope-intercept form.

Learn how to find the equation of a line parallel to y = 1/7x - 10 that passes through the point (2, -1). This step-by-step guide uses key algebraic concepts, including the point-slope form and slope-intercept form. Suitable for students in Grades 8-10.

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