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Question

Answer
Find the equation of a line parallel to 2x + 5y = 10 that passes through the point
(-5,1).
2x - 5y = -15
-5x + 2y = 27
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11:30 PM
1100021
B

Answer 1

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

Explanation:

Pre-Solving

We are given that a line is parallel to 2x + 5y = 10 and passes through (-5,1), and we want to write the equation of it.

There are 3 ways to write the equation of the line: slope - intercept form, point - slope form, and standard form.

As the question doesn't specify which form, any one of the forms is alright. However, let's write the equation in slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.

Recall that parallel lines have the same slopes.

Solving

So, we should first find the slope of 2x + 5y = 10.

The slope of the line in an equation written in standard form can be found using the formula
`-(a)/(b)`.

In this equation, a is 2 and b is 5.

So, this means the slope of the line is
`-(2)/(5)`.

It's also the slope of the line we want to find.

So, replace m with
`-(2)/(5)`.

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

Now, we need to find b.

As the equation passes through (-5,1), we can use the values to help find b.

Substitute -5 as x and 1 as y.

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

1 = 2 + b

Subtract 2 from both sides.

-1 = b

The equation in slope-intercept form is:

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