Question

Line a is formed by using the points -1,6 and 3,-2 Line B is formed by using the point -3,0 and 5,4.What linear equations can be used to represent each line

Answer 1

y = -x + 5

y = x/2 + 3/2

Explanation:

First we calculate the slope as difference between coordinates

a) P₁ ( -1 , 6 ) P₂ ( 3 , 2 )

m = Δy/Δx ⇒ m = ( y₂ - y₁ ) / ( x₂ - x₁ ) ⇒ m = (2 -6 ) / (3 -(-1))

m = -4 /4

m = -1

Now we have:

y - y₁ = m ( x - x₁ ) ⇒ y - 6 = (-1) ( x - (-1))

y - 6 = -1 * ( x + 1 ) ⇒ y - 6 = - x - 1

y = -x + 5

In the second case

Q₁ ( -3 , 0 ) Q₂ ( 5 , 4 )

Again we calculate the slope

m = Δy / Δx ⇒ m = ( 4 - 0 ) / ( 5 - (-3)) ⇒ m = 4 / 8 ⇒ m = 1/2

m = 1/2 or x = 0,5

And

y - y₁ = 1/2 ( x - x₁ ) ⇒ y - y₁ = 1/2 ( x - (-3)) ⇒ y - 0 = 1/2 * x + 3/2

y = x/2 + 3/2