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.

Parallel to the line 
2x + 5y = 10

And passes through the point (-5,1) 

First we need to identify the slope of the equation/expression 
2x + 5y = 10
To do so, you may use the slope formation (isolate y) 
5y = -2x + 10
y = (-2/5)x + 2

So the slope is -2/5
And since they mentioned the other line will be parallel then the slopes are identical. 

Passes through (-5,1)
Use the formula 

y - y1 = m(x - x1)
where m is slope 
And subsitute 
y - 1 = (-2/5)(x + 5)
y - 1 = (-2/5)x - 2 
y = (-2/5)x -1

Since the slopes are both identical then the lines are indeed parallel 
Therefore the answer is correct!