Answer:
C: The Same Line
Step-by-step explanation:
So to start we need to first know what makes lines parallel or perpendicular. Two parallel lines will have the same slope, but different y-intercepts because we know they never cross. Two perpendicular lines will have opposite-reciprocal slopes, because we know that they intersect at a right angle.
Then, we need to know the slope-intercept form of an equation. The slope intercept form is [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope of the line and [tex]b[/tex] is the y-intercept. We can see that neither equation is in this form, so we have to convert it.
Starting with the first, (I assume despite the typo) we have [tex]25y+10x= 200[/tex]
So we need to isolate the [tex]y[/tex] from everything else.
First, we'll subtract [tex]10x[/tex] from both sides of the equal sign to get [tex]25y=-10x+200[/tex]
Second, we'll divide both sides by [tex]25[/tex] to get [tex]y=-\frac{2}{5} x+8[/tex]
This means that [tex]-\frac{2}{5}[/tex] is the slope and [tex]8[/tex] is the y-intercept of the first line.
Now onto the second we have [tex]5y+2x=40[/tex] so we're going to follow the same steps to isolate [tex]y[/tex].
First, we'll subtract [tex]2x[/tex] from both sides to get [tex]5y=-2x+40[/tex]
Second, we'll divide both sides by [tex]5[/tex] to get [tex]y=-\frac{2}{5}x +8[/tex]
This means that [tex]-\frac{2}{5}[/tex] is the slope and [tex]8[/tex] is the y-intercept of the second line.
Since both of the lines have a slope [tex]-\frac{2}{5}[/tex] we know that they are parallel, so we need to check to check if they're the same by looking at the y-intercept. We can see that [tex]8[/tex] is the y-intercept of both lines, so they would be the same line.
