Question

What is the slope of the line parallel to the line with equation \[2x-5y=9\] ?

Answer 1

Hint: Try to think of the various forms of the equation of the line in order to find the slope of the given line and remove the fraction if present in the equation. Slope intercept form of equation would be used and properties of parallel lines.

Complete step by step solution:
We know that the slope of the two parallel lines is the same by definition. So, in order to find the slope of the parallel line to the given line we need to find the slope of the given line only.
Now in order to find the slope of the line we need to write the given equation \[2x-5y=9\] into slope intercept form of equation which is $y=mx+b$ where m is the slope of the line and b is said to be the y-intercept of the line.
We can convert it \[2x-5y=9\]by subtracting 2x from both the left-hand side and right-hand side of
the equation as:
$\begin{align}
  & \Rightarrow -2x+2x-5y=-2x+9 \\
 & \Rightarrow 0-5y=-2x+9 \\
 & \Rightarrow -5y=-2x+9 \\
 & \\
\end{align}$
Now dividing the above equation by -5 in order to get the variable y with coefficient 1 we get,
$\begin{align}
  & \Rightarrow \dfrac{-5y}{-5}=\dfrac{-2x+9}{-5} \\
 & \Rightarrow \dfrac{-5}{-5}y=\dfrac{-2x}{-5}+\dfrac{9}{-5} \\
 & \Rightarrow y=\dfrac{2}{5}x-\dfrac{9}{5} \\
\end{align}$
Now we can see that the slope of the line is $\dfrac{2}{5}$ and the y-intercept of the line is $\dfrac{-9}{5}$ .
Since the slope of the given line is $\dfrac{2}{5}$therefore the slope of the line parallel to the given line would be $\dfrac{2}{5}$ .

Note: In this case mostly we get stuck as we forget to think that we need to convert the equation of the line into another form in order to get the solution. Apart from this don’t get confused in the forms and the slope and the y-intercept.