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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.

y = −x − 1
2x + 5y = −5
y = −x − 3
2x + 5y = −15
y − 1= −(x + 5)
A B and E i took the test

Respuesta :

Answer:

A

Step-by-step explanation:

carlosego

For this case we have that if two lines are parallel, then their slopes are equal.

[tex]m_ {1} = m_ {2}[/tex]

We have the line given by:

[tex]2x + 5y = 10[/tex]

Rewriting:[tex]y = \frac {10-2x} {5}\\y = - \frac {2} {5} x + 2[/tex]

So, the slope is given by:

[tex]- \frac {2} {5}[/tex]

So, we have the following equation:

[tex]y = - \frac {2} {5} x + b[/tex]

We substitute the given point to find the cut point:

[tex]1 = - \frac {2} {5} (- 5) + b\\1 = 2 + b\\b = -1[/tex]

So, we have:

[tex]y = - \frac {2} {5} x-1[/tex]

Rewriting:

[tex]y + 1 = - \frac {2} {5} x\\5y + 5 = -2x\\2x + 5y = -5[/tex]

Answer:

Option B

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