Question

What is the equation of a line that is parallel to the line 2x + 5y = 10 and passes through the point (–5, 1)? Check all that apply.

Answer 1

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

Explanation:

First, we can put the equation into y = mx + b form:

2x + 5y = 10

5y = -2x + 10

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

Now, we know the slope is -
`(2)/(5)`. A parallel line will have the same slope.

So, we can plug in the point (-5, 1) into the equation y = -
`(2)/(5)`x + b to find b:

1 = -
`(2)/(5)`(-5) + b

1 = 2 + b

-1 = b

So, the equation will be y = -
`(2)/(5)`x - 1