Question

Write the equation for the family of lines with the following characterizing property(a) parallel to x + y = 10

Answer 1

We have the following:

(a)

when two lines are parallel, the slope is the same.

The slope is the constant value that is with x

`\begin{gathered} x+y=10 \\ m=1 \\ \text{therefore} \\ x+y=5 \end{gathered}`

(b)

when it is perpendicular the slope is the opposite, therefore

`\begin{gathered} 3x+2y=7 \\ m=3 \\ \text{therefore} \\ -(1)/(3)x+2y=7 \end{gathered}`