Question

What is an equation of a line that passes through the point (3,1) and it’s parallel to the line 2x+3y=24

Answer 1

2x + 3y = 9

Explanation:

the equation of a line in slope- intercept form is

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

given

2x + 3y = 24 ( subtract 2x from both sides )

3y = - 2x + 24 ( divide through by 3 )

y = -
`(2)/(3)` x + 8 ← in slope- intercept form

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

• Parallel lines have equal slopes , then

y = -
`(2)/(3)` x + c ← is the partial equation of the parallel line

to find c, substitute (3, 1 ) into the partial equation

1 = -
`(2)/(3)` (3) + c = - 2 + c ( add 2 to both sides )

3 = c

y = -
`(2)/(3)` x + 3 ← equation of parallel line in slope- intercept form

multiply through by 3

3y = - 2x + 9 ( add 2x to both sides )

2x + 3y = 9 ← equation of parallel line in standard form