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in Co-ordinate Geometry by (46.9k points)
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Find the slopes of the lines passing through the given points.

i. L (-2, -3), M (-6, -8) 

ii. E (-4, -2), F (6, 3) 

iii. T (0, -3), s (0,4)

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i. L (x1 , y1 ) = L (-2, -3) and M (x2 ,y2 ) = M (-6, -8) 

Here, x1 = -2, x2 = – 6, y1 = – 3, y2 = – 8

Slope of line LM = (y2 - y1)/ (x2 - x1)

= (-8 - (-3))/(-6 -(-2)) = (-8 + 3)/ (-6 + 2)

= -5/-4 = 5/4

∴ The slope of line LM is 5/4

ii. E (x1 , y1 ) = E (-4, -2) and F (x2 , y2 ) = F (6, 3) 

Here,x1 = -4, x2 = 6, y1 = -2, y2 = 3

Slope of line EF = (y2 - y1)/ (x2 - x1)

= (3 - (-2))/(6 - (-4)) = (3+2)/(6 + 4)

= 5/10 = 1/2

The slope of line EF is 1/2.

iii. T (x1 , y1 ) = T (0, -3) and S (x2 , y2 ) = S (0, 4) 

Here, x1 = 0, x2 = 0, y1 = -3, y2 = 4

Slope of line TS  = (y2 - y1)/(x2 - x1)

= (4 - 9(-3))/(0 - 0) = (4 +3)/0 = 7/0

= Not definned

∴ The slope of line TS cannot be determined.

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