Question

| 10. Write an equation of a line that is parallel to

the line-3x + 4y = 5 and passes through the
point (2.1)
​

Answer 1

see explanation

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange - 3x + 4y = 5 into this form

Add 3x to both sides

4y = 3x + 5 ( divide all terms by 4 )

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

with slope m =
`(3)/(4)`

• Parallel lines have equal slopes, thus

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

To find c substitute (2. 1) into the partial equation

1 =
`(3)/(2)` + c ⇒ c = -
`(1)/(2)`

y =
`(3)/(4)` x -
`(1)/(2)` ← equation of parallel line