Which equation produces a line that is parallel to the line represented by the function below?
y= 2/5x + 9
a. y= 5x + 2y = 4
b. y= 2x - 5y = 8
c. y= 5x - 2y = -3
d. y= 2x + 5y = -7

B.

I ignored the extra y= part in each equation.

Step-by-step explanation:

The line given is in slope-intercept form, y=mx+b where m is slope and b is y-intercept.

Parallel lines have the same slope.

So the slope of y=(2/5)x+9 is m=2/5.

So we are looking for a line with that same slope.

In slope-intercept form the line would by y=(2/5)x+b where we do not know b since we weren't given a point.

So all of the choices are written in standard form ax+by=c where a,b, and c are integers.

We want integers so we want to get rid of that fraction there.  To do that we need to multiply both sides of y=(2/5)x+b for 5.  This gives us:

5y=2x+5b

Subtract 2x on both sides:

-2x+5y=5b

Now of the coefficients of x in your choices is negative like ours is. So I'm going to multiply both sides by -1 giving us:

2x-5y=-5b

Compare

2x-5y=-5b to your equations.

A doesn't fit because it's left hand side is 5x+2y.

B fits because it's left hand side is 2x-5y.

C doesn't fit because it's left hand side is 5x-2y.

D doesn't fit because it's left hand side is 2x+5y.

I ignored all the extra y= parts in your equations.

5

step-by-step explanation: