Question

Directions: find the equation of each line in standard form with the given properties:

1. Slope =3, y-intercept=1
2. Passing through (0,2), slope = -4
3. Passing through (-1,3) and (1,1)
4. Passing through (1,3), slope = 1/2
5. Passing through (1/2,1) and (4,2)

Answer 1

Explanation:

1) slope = 3 ; y-intercept = 1

y = mx + b

y = 3x + 1

0 = 3x + 1 -y

-1 = 3x - y

ANS: 3x - y = -1

2) Passing through (0,2), slope = -4

y - y₁ = m(x -x₁)

y - 2 = -4(x - 0)

y - 2 = -4x

4x + y - 2 = 0

Ans: 4x + y = 2

3)Passing through (-1,3) and (1,1)

Slope =
`(y_(2)-y_(1))/(x_(2)-x_(1))`

`= (1-3)/(1-[-1])\\\\= (-2)/(1+1)\\\\= (-2)/(2)\\\\= - 1`

m= -1 ; (-1 , 3)

y - y₁ = m(x -x₁)

y - 3 = (-1)(x - [-1] )

y -3 = (-1)(x +1 )

y - 3 = -x - 1

x + y -3 = -1

x +y = -1 + 3

Ans: x + y = 2

4) Passing through (1,3), slope = 1/2

y - y₁ = m(x -x₁)

`y - 3 = (1)/(2)(x - 1)\\\\y - 3 = (1)/(2)x - (1)/(2)\\\\`

Multiply the equation by 2

`2*y - 2*3 = 2*(1)/(2)x - 2*(1)/(2)\\\\2y - 6 = x - 1\\`

2y - 6 +1 = x

2y - 5 = x

-5 = x - 2y

Ans: x - 2y = -5

5) Passing through (1/2,1) and (4,2)

Slope =
`(2-1)/(4-(1)/(2))`

`= (1)/((7)/(2))\\\\= (2)/(7)`

m = 2/7 ; (4 , 2)

y - y₁ = m(x -x₁)

`y - 2 = (2)/(7)(x - 4)\\\\7y - 7*2 = 7*(2)/(7)(x - 4)\\\\7y - 14 = 2(x -4)\\\\7y - 14 = 2x - 8\\\\`

7y - 14 + 8 = 2x

7y - 6 = 2x

Ans: 2x - 7y = -6