Question

I need help finding the equation to the parallel line

Answer 1

The first thing we have to know is that parallel lines have the same slope. The slope can be identified in the general equation of the line:

`\begin{gathered} y=mx+b \\ m\to\text{slope} \\ b\to y-\text{intercept} \end{gathered}`

Taking that into account, we identify the slope of the given line

`\begin{gathered} y=-(2)/(3)x+(3)/(2) \\ m=-(2)/(3) \\ b=(3)/(2) \end{gathered}`

Now we replace the slope in the general equation

`y=-(2)/(3)x+b`

With the given point we can find the intercept value of y and thus be able to have the equation of our parallel line

`\begin{gathered} (4,-7)\to\text{given point} \\ -7=-(2)/(3)(4)+b \\ b=-7+(8)/(3) \\ b=-(13)/(3) \end{gathered}`

The equation of the parallel line that passes through the point (4, -7) is

`y=-(2)/(3)x-(13)/(3)`

using the slash it would be: y = 2/3x-13/3