Question

What line is parallel to 2x+5y=6 that goes through (5,3)

Answer 1

4y = x - 17

Explanation:

First off, in the equation given : 2x + 5y = 6 , make y the subject of the formula which will give y =
`(-2x)/(5)` +
`(6)/(5)` which make the gradient, m, the coefficient of x =
`(-2)/(5)` . Since the line we're looking for is parallel to the one we were given, their respective gradients would be the same. (If they were perpendicular, the gradient of the new line would be a negative inverse of the given line)

Then you proceed to use the one-point formula : y - y₀ = m(x - x₀), where y₀ = 3 and x₀ = 5 from the point it goes through (5, 3)

y - 3 =
`(1)/(4)`(x - 5); y - 3 =
`(x)/(4)` -
`(5)/(4)`; y =
`(x)/(4)` -
`(5)/(4)` +3

y =
`(x)/(4)` -
`(17)/(4)`; y =
`(x-17)/(4)` ; 4y = x - 17