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=\frac{-7}{-9}x+\frac{9}{(-9)} \\ \\ y=\frac{7}{9}x-\frac{9}{9} \\ \\ y=\frac{7}{9}x-1 \end{gathered}$

You can identify that its slope is:

$m=\frac{7}{9}$

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:

$y=\frac{7}{9}x+1$

Hence, the answers are:

(a)

$y=x+6$

(b)

$y=\frac{7}{9}x+1$