Question

How do you find the slope given \[8x - 5y = 4\]?

Answer 1

Hint: The general standard equation of a straight line is given by the formula \[y = mx + c\] where \[m\] is the slope of the straight line, in the question we are given with equation of a straight line so we will compare the given equation with the general standard equation of a straight line and then find the slope of the given line.

Complete step by step solution:
Given,
\[8x - 5y = 4\]
On rewriting the above equation to the standard from of line equation which is
\[y = mx + c\]
Where m is slope here and c is constant
\[8x - 5y = 4\]
Moving the y term to right hand side we will get
\[8x - 4 = 5y\]
Now dividing with 5 on both sides we will get
\[
  \dfrac{{8x}}{5} - \dfrac{4}{5} = y \\
   \Rightarrow y = \dfrac{{8x}}{5} - \dfrac{4}{5} \\
 \]
Now on comparing the above line equation with the standard line equation \[y = mx + c\], we get
\[ m = \dfrac{8}{5} \]
$ \Rightarrow c = \dfrac{4}{5} $

Therefore the slope of the given equation will be \[m = \dfrac{8}{5}\]

Additional information :
If you are provided with the line equation, then it is not a big deal to find the slope you can easily find the slope, but when you are provided with two points to find the slope then you have to use the formula
Slope \[ = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]
Even if you can find the point on the line by substituting \[x = 0\] you will get the first point and substitute \[y = 0\] for the second point and use the above formula.

Note: Slope of a line is the ratio of the change in the y-axis with respect to the x-axis and it can be either positive or negative. For a horizontal line the slope of the line will be zero i.e.\[m = 0\] and for a vertical line the slope of the line is undefined.