Question

using the point slope form y-y1 = m(x-x1) write an equation for the line parallel to 2x-3y = 7 and passes through 5,1

Answer 1

y - 1 =
`(2)/(3)` (x - 5)

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercpt )

given

2x - 3y = 7 ( subtract 2x from both sides )

- 3y = - 2x + 7 ( divide through by - 3 )

y =
`(2)/(3)` x -
`(7)/(3)` ← in slope- intercept form

with slope m =
`(2)/(3)`

• Parallel lines have equal slopes

then the equation of a parallel line in point- slope form

with m =
`(2)/(3)` and (x₁, y₁ ) = (5, 1)

y - 1 =
`(2)/(3)` (x - 5)