The equation for line j can be written as y=
–
5
7
x–10. Line k, which is parallel to line j, includes the point (
–
9,5). What is the equation of line k?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.


The equation of line \( j \) is given as:

\[
y = -\frac{5}{7}x - 10
\]

Since line \( k \) is parallel to line \( j \), it will have the same slope. The slope of line \( j \) is \( -\frac{5}{7} \), so the slope of line \( k \) is also \( -\frac{5}{7} \).

Now, we use the point-slope form of a line equation to find the equation of line \( k \). The point-slope form is:

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

where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line. For line \( k \), \( m = -\frac{5}{7} \) and the given point is \( (-9, 5) \).

Substitute the values:

\[
y - 5 = -\frac{5}{7}(x + 9)
\]

Now, distribute the slope on the right-hand side:

\[
y - 5 = -\frac{5}{7}x - \frac{5}{7} \times 9
\]

\[
y - 5 = -\frac{5}{7}x - \frac{45}{7}
\]

Next, add 5 to both sides:

\[
y = -\frac{5}{7}x - \frac{45}{7} + 5
\]

Convert 5 to a fraction with denominator 7:

\[
5 = \frac{35}{7}
\]

Now add the fractions:

\[
y = -\frac{5}{7}x - \frac{45}{7} + \frac{35}{7}
\]

\[
y = -\frac{5}{7}x - \frac{10}{7}
\]

Thus, the equation of line \( k \) in slope-intercept form is:

\[
y = -\frac{5}{7}x - \frac{10}{7}
\]

Would you like a more detailed explanation of the steps?

### Related Questions:
1. How do you find the slope of a line from two points?
2. What is the relationship between parallel lines and their slopes?
3. How can you convert a point-slope equation into slope-intercept form?
4. What is the general form of a linear equation, and how does it differ from slope-intercept form?
5. How do you find the equation of a line perpendicular to a given line?

**Tip:** For parallel lines, always ensure their slopes are identical.

The equation for line j can be written as y = -(5/7)x - 10. Line k, which is parallel to line j, includes the point (-9, 5). What is the equation of line k? 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 another, given its slope and a point it passes through. This problem explores key algebraic concepts, including parallel lines, point-slope form, and slope-intercept form. Suitable for students in Grades 8-10.

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