Question

Instructions: Find the equation of the line through point (2, -1) and

parallel to 2x + 5y = 15. Use a forward slash (i.e. "/") for fractions (e.g. 1/2
for 3).

Answer 1

`y = -(2)/(5)x -(1)/(5)`

Explanation:

Given

Passes through:
`(2,-1)`

Parallel to:
`2x + 5y = 15`

Required

First, calculate the slope of the parallel line

`2x + 5y = 15`

Make y the subject

`5y = 15 - 2x`

Divide through by 5

`y = 3 - (2)/(5)x`

`y =- (2)/(5)x+3`

An equation in slope intercept has the form:

`y = mx + b`

Where:

m = slope

`y = mx + b`

So:

`m = -(2)/(5)`

The required is parallel to
`2x + 5y = 15`.

This mean, the same slope

The equation is the calculated using:

`y - y_1 = m(x - x_2)`

This gives:

`y - (-1) = -(2)/(5)(x - 2)`

`y +1 = -(2)/(5)x +(2)/(5)*2`

`y +1 = -(2)/(5)x +(4)/(5)`

`y = -(2)/(5)x +(4)/(5)-1`

Take LCM

`y = -(2)/(5)x +(4-5)/(5)`

`y = -(2)/(5)x -(1)/(5)`

i.e.

`y = -2/3x -1/5`