Question

Write the equation of the line that is parallel to 5x - 2y =16 and passes through (10,5).

Answer 1

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.

$5x - 2y = 16$

We need to get it to look like

$y = mx + b$

So we need to isolate our y value.

In order to do this, we do basics of Algebra

$- 2y = 16 - 5x$

$y = \frac{16 - 5x}{ - 2}$

$y = - 8 + \frac{5}{2} x$

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

$y - {y} _{1} = m( x - x _{1})$

where m is our slope and (x1,y1) is our given point.

Subsitue

$y - 5 = \frac{5}{2} (x - 10)$

$y - 5 = \frac{5}{2} x - 25$

Add 5 to both sides

$y = \frac{5}{2} x - 20$