Question

The lines represented by the equations 25y

Answer 1

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 $y=mx+b$ where $m$ is the slope of the line and $b$ 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 $25y+10x= 200$

So we need to isolate the $y$ from everything else.

First, we'll subtract $10x$ from both sides of the equal sign to get $25y=-10x+200$

Second, we'll divide both sides by $25$ to get $y=-\frac{2}{5} x+8$

This means that $-\frac{2}{5}$ is the slope and $8$ is the y-intercept of the first line.

Now onto the second we have $5y+2x=40$ so we're going to follow the same steps to isolate $y$.

First, we'll subtract $2x$ from both sides to get $5y=-2x+40$

Second, we'll divide both sides by $5$ to get $y=-\frac{2}{5}x +8$

This means that $-\frac{2}{5}$ is the slope and $8$ is the y-intercept of the second line.

Since both of the lines have a slope $-\frac{2}{5}$ 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 $8$ is the y-intercept of both lines, so they would be the same line.