Question

1. The lines y = -x – 3 and y = -x - 5 are parallel. What is the value of a? (2 points) (A) a = -2 (B) 1 a = (C) Q= - (D) a=-9

Answer 1

Given equation of lines :

`\begin{gathered} y=-(2)/(3)x-3 \\ y=(3)/(a)x-5 \end{gathered}`

Since the lines are parallel

From the propertoes of parallel lines, the slope of parallel lines are always equal,

where in the general equation of line

`\begin{gathered} y=m(x-a)+b \\ m\text{ is the slope} \end{gathered}`

On comapring the the first equation of line with general equation of line

we get m=-2/3

so, slope of first line is -2/3

similarly on comparing second equation of line with the general equation of line,

we get m=3/a

so, slope of second line is 3/a

since slope of both the lines are equal because they are paralle,

`\begin{gathered} \text{slope first line = slope of second line} \\ (-2)/(3)=(3)/(a) \\ \text{apply cross multiplication and then solve for a,} \\ -2a=3*3 \\ -2a=9 \\ a=-(9)/(2) \end{gathered}`

So, the value of a is -9/2

Answer : C. -9/2