Question

zipit - 3. Find the equation of a line passing through (5, -6) parallel to:c) x + 3y=8 (e) x=7 (b) 3x + 5y = 7 (d) 7x - 12y = 5 (f) 2y = 5

Answer 1

Equation of a line passing through the point (5, -6) and parallel to 3x + 5y = 7

First find the slope of the equation 3x + 5y = 7

Re-arrange

5y = -3x + 7

Divide through by 5

`y=-(3)/(5)\text{x + }(7)/(5)`

compare the above with y = mx + b

slope (m) = -3/5

Parallel equations have same slope

The slope of the equatiion is -3/5

substitute

x₁ = 5 y₁=-6 m=-3/5 in the formula below

y- y₁ = m(x - x₁)

`y+6=-(3)/(5)(x\text{ -5)}`

`y\text{ + 6 =}(-3)/(5)x\text{ +3}`
`(3)/(5)x\text{ + y = 3-6}`
`(3)/(5)x+y=-3`

`3x+\text{ 5y =-15}`