Question

What is the slope of the dashed line?What is the slope of any line parallel to the dashed line?find the equation for the parallel line that passed through (1,1)

Answer 1

You can identify the slope (m) of a line with the equation written in the form y=mx+b

Dashed line:

`-6x+7y=-14`

Write the equation in the form y=mx+b (solve y):

`\begin{gathered} 7y=6x-14 \\ y=(6)/(7)x-(14)/(7) \\ \\ y=(6)/(7)x-2 \end{gathered}`

The slope of the dashed line is: 6/7

`m=(6)/(7)`

Two parallel lines have the same slope.

Then, the slope of any line parallel to the dashed line is: 6/7

________________________

Find the equation of a parallel line that passes through (1,1)

The parallel line needs to have slope (m=6/7)

Uses the given point and the slope to find the y-intercept (b) in the equation y=mx+b:

`\begin{gathered} y=mx+b \\ 1=(6)/(7)(1)+b \\ \\ 1=(6)/(7)+b \\ \\ 1-(6)/(7)=b \\ \\ (7-6)/(7)=b \\ \\ (1)/(7)=b \\ \\ \\ b=(1)/(7) \end{gathered}`

Then, the equation of a parallel line that passes through (1,1) is:

`y=(6)/(7)x+(1)/(7)`