Question

What is the equation of the line parallel to 3x + 5y = 11 that passes through the point (15, 4)?

O y = -29
= 8x
2 O yx-
y = 3x-21
O x- Ex+5
Oy-+13


Please help!!

Answer 1

The equation of the line is
`y = -(3x)/(5) + 13`

Explanation:

Equation of a line:

The equation of a line has the following format:

`y = mx + b`

In which m is the slope and b is the y-intercept.

Parallel lines:

If two lines are parallel, their slopes are the same.

Parallel to 3x + 5y = 11

Placing in the standard format:

`5y = -3x + 11`

`y = -(3x)/(5) + (11)/(5)`

So the slope is
`-(3)/(5)`, which means that the desired equation is:

`y = -(3x)/(5) + b`

Passes through the point (15, 4).

This mean that when
`x = 15, y = 4`. We use this to find b. So

`y = -(3x)/(5) + b`

`4 = -(3(15))/(5) + b`

`-9 + b = 4`

`b = 13`

So

`y = -(3x)/(5) + 13`