Line t has an equation of y–3=
–
1
6
(x+7). Parallel to line t is line u, which passes through the point (
–
4,
–
2). What is the equation of line u?

To find the equation of line \( u \) that is parallel to line \( t \), we first identify the slope of line \( t \). The given equation is:

\[
y - 3 = -\frac{1}{6}(x + 7)
\]

This can be rewritten in slope-intercept form \( y = mx + b \):

\[
y = -\frac{1}{6}x - \frac{7}{6} + 3 \\
y = -\frac{1}{6}x + \frac{11}{6}
\]

The slope (\( m \)) of line \( t \) is \( -\frac{1}{6} \). Since line \( u \) is parallel to line \( t \), it has the same slope.

Using the point \( (-4, -2) \) and the slope \( -\frac{1}{6} \), we use point-slope form:

\[
y - y_1 = m(x - x_1) \\
y + 2 = -\frac{1}{6}(x + 4)
\]

Simplifying this gives:

\[
y + 2 = -\frac{1}{6}x - \frac{2}{3} \\
y = -\frac{1}{6}x - \frac{2}{3} - 2 \\
y = -\frac{1}{6}x - \frac{8}{3}
\]

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

\[
y = -\frac{1}{6}x - \frac{8}{3}
\]

Would you like further details or have any questions? Here are some related questions:

1. How do you convert between different forms of line equations?
2. What is the significance of parallel lines in geometry?
3. Can you explain how to find the equation of a line given two points?
4. What happens to the slope when lines are perpendicular?
5. How can you graph linear equations effectively?

**Tip:** Always confirm the slope when determining parallel lines!

Line t has an equation of y–3=-1/6(x+7). Parallel to line t is line u, which passes through the point (-4,-2). What is the equation of line u?

Learn how to find the equation of a line parallel to another given line. This example covers the equation of line t, its slope, and how to use point-slope form to determine the equation of line u passing through (-4,-2). Ideal for students in Grades 8-10.

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