Question

Find the slope of a line that is parallel to the following line: 6y – 5x = 9

Answer 1

Given the line:

`6y-5x=9`

You need to remember the Slope-Intercept Form of the equation of a line:

`y=mx+b`

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

In order to write the given equation in Slope-Intercept Form, you have to solve for "y":

`\begin{gathered} 6y=5x+9 \\ \\ y=(5)/(6)x+(9)/(6) \\ \\ y=(5)/(6)x+(3)/(2) \end{gathered}`

Notice that:

`m=(5)/(6)`

By definition, the slopes of parallel lines are equal. Therefore, the slope of a line parallel to the given must be:

`m=(5)/(6)`

Hence, the answer is:

`m=(5)/(6)`