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

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!

Answer 2

y = −x − 1

2x + 5y = −5

y − 1= −(x + 5)