Find the slopes of the lines passing through the given points. i. A (

1.	Find the slopes of the lines passing through the given points. i. A (2, 3), B (4, 7) ii. P(-3, 1), Q (5, -2) iii. C (5, -2), D (7, 3)
Answer» i. A (x₁ , y₁ ) = A (2, 3) and B (x₂ , y₂ ) = B (4, 7) Here, x₁ = 2, x₂ = 4, y₁ = 3, y₂ = 7 Slope of line AB = (y₂ - y₁)/(x₂ - x₁) =(7 - 3)/(4 - 2) = 4/2 = 2 ∴ The slope of line AB is 2. ii. P (x₁ , y₁ ) = P (-3, 1) and Q (x₂ , y₂ ) = Q (5, -2) Here, x₁ = -3, x₂ = 5, y₁ = 1, y₂ = -2 Slope of line PQ = (y₂ - y₁)/(x₂ - x₁) = (-2 - 1)/(5 - (-3)) = -3/(5+3) = -3/8 The slope of line PQ is -3/8 iii. C (x₁ , y₁ ) = C (5, -2) and D (x₂ , y₂ ) = D (7, 3) Here, x₁ = 5, x₂ = 7, y₁ = -2, y₂ = 3 Slope of line CD = (y₂ - y₁)/(x₂ - x₁) = (3 - (-2))/ (7 - 5) = (3 + 2)/2 = 5/2 ∴The slope of line CD is 5/2

Find the slopes of the lines passing through the given points. i. A (2, 3), B (4, 7) ii. P(-3, 1), Q (5, -2) iii. C (5, -2), D (7, 3)

Answer»

i. A (x₁ , y₁ ) = A (2, 3) and B (x₂ , y₂ ) = B (4, 7)

Here, x₁ = 2, x₂ = 4, y₁ = 3, y₂ = 7

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

=(7 - 3)/(4 - 2)

= 4/2 = 2

∴ The slope of line AB is 2.

ii. P (x₁ , y₁ ) = P (-3, 1) and Q (x₂ , y₂ ) = Q (5, -2)

Here, x₁ = -3, x₂ = 5, y₁ = 1, y₂ = -2

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

= (-2 - 1)/(5 - (-3))

= -3/(5+3) = -3/8

The slope of line PQ is -3/8

iii. C (x₁ , y₁ ) = C (5, -2) and D (x₂ , y₂ ) = D (7, 3)

Here, x₁ = 5, x₂ = 7, y₁ = -2, y₂ = 3

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

= (3 - (-2))/ (7 - 5)

= (3 + 2)/2 = 5/2

∴The slope of line CD is 5/2

Discussion

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