Question

Write the equation of the line parallel to Y equals 2/3X +1 through the point (0,-4)  use slope intercept form

Answer 1

Writing the slope-intercept form of a linear equation, we have:

`y=mx+b`

Where m is the slope and b is the y-intercept.

Since parallel lines have the same slope, we can see that the slope of the line y = 2/3x + 1 is equal m = 2/3, so for our equation we also have m = 2/3.

Now, using the point (0, -4), we have:

`\begin{gathered} y=(2)/(3)x+b \\ (0,-4)\colon \\ -4=(2)/(3)\cdot0+b \\ b+0=-4 \\ b=-4 \end{gathered}`

So our equation is:

`y=(2)/(3)x-4`

y = 2/3x - 4