Respuesta :
Answer:
B
Step-by-step explanation:
Parallel lines have same slope. Parallel means to never intersect. So if something has to not intersect, they must have similar slopes but from a different starting position.
So Parallel Lines have similar slopes.
So using the given equation let manipulate this expression to find our a slope. This looks like a linear equation in the form of Ax+By=C (standard form). So let isolate this to y=mx+b because the latter is slope intercept form, which gives us our slope which is m.
[tex]5x - 2y = 16[/tex]
We need to get it to look like
[tex]y = mx + b[/tex]
So we need to isolate our y value.
In order to do this, we do basics of Algebra
[tex] - 2y = 16 - 5x[/tex]
[tex]y = \frac{16 - 5x}{ - 2} [/tex]
[tex]y = - 8 + \frac{5}{2} x[/tex]
So our slope of the original line is 5/2. So our new Parallel lines must have this slope as well. Our new line also passes through 10,5 so since we have a point and a slope we use point slope form
[tex]y - {y} _{1} = m( x - x _{1})[/tex]
where m is our slope and (x1,y1) is our given point.
Subsitue
[tex]y - 5 = \frac{5}{2} (x - 10)[/tex]
[tex]y - 5 = \frac{5}{2} x - 25[/tex]
Add 5 to both sides
[tex]y = \frac{5}{2} x - 20[/tex]
