Question

Which statement about the following equations is correct? y=2x+5 y=−2x+5 Select one: a. The equations are dependent because the lines are the same line. b. The equations are dependent because the lines do not intersect. c. The equations are independent because the equations represent parallel lines. d. The equations are independent because the lines intersect in one point.

Answer 1

The correct answer is D.

In fact, when written in the form $y=mx+q$, $m$ represents the slope of the line, and two lines are parallel if they have the same slope.

In this case, the slopes are not the same (they are $2$ and $-2$, respectively), so option C is wrong.

And neither they are the same line, because the equations are different, so option A is wrong as well.

Finally, the lines intersect, because if you ask

$2x+5=-2x+5$

you get

$4x=0 \iff x=0$

and so $(0,5)$ is the point of intersection, and option B is wrong as well.