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Lorico [155]
2 years ago
15

Help Determine which equation is parallel to line jk and which is perpendicular to line jk.

Mathematics
1 answer:
alukav5142 [94]2 years ago
8 0

Answer:

5x + 3y = 13 parallel.

6x - 10y = 7 perpendicular.

Step-by-step explanation:

Two lines with slopes m_1 and m_2 are parallel when m_1=m_2 and are perpendicular when m_1*m_2=-1

Now determine the slope of all the lines

The line jk passes through the points

(-5,5) and (1,-5) so its slope is

\frac{-5-5}{1-(-5)}=\frac{-10}{6}=-\frac{5}{3}

To determine the slope of the lines in the blue rectangles, isolate y from each one and the coefficient of x is the slope

5x-3y = 8 ------> y = (5/3)x + 8/3 ------> slope 5/3

Neither parallel nor perpendicular.

6x+10y = 11 ------> y = (-6/10)x + 11/10 = (-3/5)x + 11/10 ------> slope -3/5

Neither parallel nor perpendicular.

5x + 3y = 13 ------> y = (-5/3)x + 13/3 ------> slope -5/3

This line is parallel

6x - 10y = 7 ------> y = (6/10)x - 7/10 = (3/5)x -7/10 ------> slope 3/5

Since (-5/3)(3/5) = -1 this line is perpendicular.

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