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

Question

asked Nov 8, 2023 152k views

1 Answer

Tmthyjames · Answer 1 · 2023-11-12T02:34:00+0000

(a) Given this equation of a line:

You need to rewrite it in Slope-Intercept Form:

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:

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

(b) Given the line:

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

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

You can identify that its slope is:

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:

Hence, the answers are:

(a)

(b)