Question

How do you find the slope given \[4x-5y=20\]?

Answer 1

Hint: The standard form of the equation of the straight line is \[ax+by+c=0\]. We can find the slope of the line by using the values of the coefficients of the equation. The slope of the line is \[\dfrac{-a}{b}\]. To find the slope of a straight line we have to convert it to its standard form.

Complete step by step answer:
We are given the equation of the straight line as \[4x-5y=20\].
We know that the standard form of the equation of the straight line is \[ax+by+c=0\], To convert a straight-line equation to its standard form, we need to take all its terms to one side of the equation leaving zero to the other side. We can do this for the given equation as follows,
Subtracting 20 from both sides of this equation \[4x-5y=20\], we get
\[\begin{align}
  & \Rightarrow 4x-5y-20=20-20 \\
 & \Rightarrow 4x-5y-20=0 \\
\end{align}\]
This is the standard form of the straight-line equation. Here, we have \[a=4,b=-5\And c=-20\]. We can find the slope of the straight-line using the coefficients of the equation as follows
The slope of the line equals \[\dfrac{-a}{b}\], substitute the values of coefficients, we get
\[\Rightarrow slope=\dfrac{-4}{-5}\]
Canceling out \[-1\] as a common factor of the numerator, and the denominator, we get
\[\Rightarrow slope=\dfrac{4}{5}\]
Hence, the slope of the line is \[\dfrac{4}{5}\].

Note:
We can also graph the straight line using the given equation as follows,

We can also convert the equation of the line to slope-intercept form \[y=mx+c\], to find the slope of the line. To convert into this form, we have to take the variable term \[y\] to one side of the equation and make its coefficient one, leaving the constant and variable \[x\] terms to another side.