Question

Write the equation of a line in standard form that passes through the point (3,-2) and is parallel to the line y=1/3x + 4

Answer 1

x - 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 )

y =
`(1)/(3)` x + 4 ← is in slope- intercept form

with slope m =
`(1)/(3)`

• Parallel lines have equal slopes , then

y =
`(1)/(3)` x + c ← is the partial equation

to find c substitute (3, - 2 ) into the partial equation

- 2 =
`(1)/(3)` (3) + c = 1 + c ( subtract 1 from both sides )

- 3 = c

y =
`(1)/(3)` x - 3 ← equation in slope- intercept form

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

multiply the equation through by 3 to clear the fraction

3y = x - 9 ( subtract x from both sides )

- x + 3y = - 9 ( multiply through by - 1 )

x - 3y = 9 ← equation in standard form