Question

Find an equation of the line that (a) has the same v-intercept as the line

Answer 1

(a) Given this equation of a line:

`y-7x-6=0`

You need to rewrite it in Slope-Intercept Form:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

You can rewrite it in this form by solving for "y":

`\begin{gathered} y-7x=6 \\ y=7x+6 \end{gathered}`

You can identify that the y-intercept is:

`b=6`

Then, you can write the following equation of a line with the same y-intercept:

`y=x+6`

(b) Given the line:

`7x-9y=9`

You can rewrite it in Slope-Intercept Form in order to identify its slope:

`-9y=-7x+9`
`\begin{gathered} y=(-7)/(-9)x+(9)/((-9)) \\ \\ y=(7)/(9)x-(9)/(9) \\ \\ y=(7)/(9)x-1 \end{gathered}`

You can identify that its slope is:

`m=(7)/(9)`

By definition, the slopes of parallel lines are equal, but the y-intercepts are different.

Therefore, knowing this, you can write the following equation of a line parallel to the line given in the exercise:

`y=(7)/(9)x+1`

Hence, the answers are:

(a)

`y=x+6`

(b)

`y=(7)/(9)x+1`