Question

How do you find the slope given \[6x + 2y = 4\] ?

Answer 1

Hint: Rewrite the given line equation to standard straight line equation i.e. \[y = mx + c\] and then compare the terms of the given equation to find the slope of the given equation, where m is the slope.

Complete step by step solution:
Given the line equation,
\[6x + 2y = 4\]
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
\[6x + 2y = 4\]
Moving x term to right hand side we will get
\[2y = 4 - 6x\]
Now dividing with 2 on both side we will get
\[y = \dfrac{4}{2} - \dfrac{{6x}}{2}\]
On simplifying the equation we will get
 \[
   \Rightarrow y = 2 - 3x \\
   \Rightarrow y = - 3x + 2 \\
 \]
Now on comparing the above line equation with the standard straight line equation \[y = mx + c\] , we will get
 \[
   \Rightarrow m = - 3 \\
   \Rightarrow c = 2 \\
 \]

Therefore the slope of the given equation is \[m = - 3\] .

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 describes the steepness of a line and it can be either positive or negative, if the slope of is high then it tell that the line has greater steepness, to find the slope all you need to do is to make the given line equation into standard format and then compare the values to get the slope of a line.