Question

What is the equation of the line that is parallel to the given line and passes through the point (−3, 2)?

3x − 4y = −17
3x − 4y = −20
4x + 3y = −2
4x + 3y = −6

Answer 1

4x + 3y = - 6

Explanation:

the equation of a line in slope- intercept form is

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

• Parallel lines have equal slopes

calculate the slope of the line using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (3, - 1) ← 2 points on the line

m =
`(-1-3)/(3-0)` =
`(-4)/(3)` = -
`(4)/(3)` , then

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

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

2 = 4 + c ⇒ c = 2 - 4 = - 2

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

multiply through by 3 to clear the fraction

3y = - 4x - 6 ( add 4x to both sides )

4x + 3y = - 6 ← in standard form