:- Given equation of line M: y X-9 -6- Line L is parallel to line M and it passes through the point (6, 5). Write the equation of line L.

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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Write the equation of line L
**Given Equation of Line M:**

\[ y = \frac{5}{3}x - 9 \]

Line L is parallel to line M and it passes through the point (6, 5).

**Task:**

Write the equation of line L.

---

*Explanation:*

To find the equation of line L, which is parallel to line M, we need to use the same slope because parallel lines have the same slope. The slope of line M is \(\frac{5}{3}\).

Using the point-slope form of a line equation \((y - y_1 = m(x - x_1))\), where \((x_1, y_1)\) is a point on the line and \(m\) is the slope, we substitute the point (6, 5) and the slope \(\frac{5}{3}\):

\[ y - 5 = \frac{5}{3}(x - 6) \]

Simplify this equation to find the equation of line L.
Transcribed Image Text:**Given Equation of Line M:** \[ y = \frac{5}{3}x - 9 \] Line L is parallel to line M and it passes through the point (6, 5). **Task:** Write the equation of line L. --- *Explanation:* To find the equation of line L, which is parallel to line M, we need to use the same slope because parallel lines have the same slope. The slope of line M is \(\frac{5}{3}\). Using the point-slope form of a line equation \((y - y_1 = m(x - x_1))\), where \((x_1, y_1)\) is a point on the line and \(m\) is the slope, we substitute the point (6, 5) and the slope \(\frac{5}{3}\): \[ y - 5 = \frac{5}{3}(x - 6) \] Simplify this equation to find the equation of line L.
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