Question

Determine whether the graphs of y=3x+5 and -y=-3x-13 are parallel, perpendicular, coincident, or none of these

Answer 1

lines are parallel not coincident not perpendicular.

Explanation:

Given equations of lines are

y=3x+5 eq(1)

-y=-3x-13

Since 2nd equation is not in the form of slope-intercept form so multiply by -1 to both sides of above equation, we get

y=3x+13 eq(2)

y=mx+b where m and b denotes slope and y-intercept respectively.

comparing above equation with eq(1) and eq(2), we get

`m_(1) =3and b_(1) =5` for eq(1)

`m_(2) =3and b_(2) =13` for eq(2)

now, slope of eq(1) and eq(2) are equal hence lines are parallel.

lines are not coincident since their intercepts are not equal.

lines are not perpendicular since their slopes are not negative reciprocals of each other.

Answer 2

Explanation:

Given lines are

`y=3x+5 :\\-y=-3x-13`

Since second equation is not in slope intercept form, let us change it to slope intercept form

`y=3x+5 :\\y=3x+13`

We see that slope of the I line is 3 and slope of II line is also 3

Since slopes are equal, we see that the lines are parallel

NOte that two lines will be parallel or coincident if slopes are equal

These two lines have same slope, but not coincident since y intercepts are different as 5 and 13

So these two lines are parallel

Not coincident and not perpendicular