Question

How do you find the slope and intercept of $ 12x + 4y - 2 = 0 $ ?

Answer 1

Hint: In order to this question, to find the slope and the intercept, we will separate any of the variables such that $ y $ from the given equation at one side and then simplify the equation in the form of $ y = mx + b $ . Then $ m $ is the slope and $ b $ is the $ y - \operatorname{int} ercept $ .

Complete step-by-step answer:
The given equation: $ 12x + 4y - 2 = 0 $
Now, we will solve the equation for $ y $ -
So, we will separate the $ y $ variable at L.H.S-
 $
   \Rightarrow 4y = 2 - 12x \\
   \Rightarrow y = \dfrac{{2 - 12x}}{4} \;
  $
Now, we will simplify the value of $ y $ until the equation will be in the form of $ y = mx + b $ :
 $
   \Rightarrow y = \dfrac{1}{2} - 3x \\
  or,\,\,\,y = - 3x + \dfrac{1}{2} \;
  $
As we can see that the above equation is in the form of $ y = mx + b $ ,
where, $ m $ is the slope (which is the coefficient of variable $ x $ )
and, $ b $ is the $ y - \operatorname{int} ercept $ or the constant.
Hence, from the equation: $ y = - 3x + \dfrac{1}{2} $
Slope, $ m = - 3 $ and
 $ y - \operatorname{int} ercept $ , $ b = \dfrac{1}{2} $ .
So, the correct answer is “ $ y = - 3x + \dfrac{1}{2} $ ”.

Note: The slope of a line indicates how quickly it is moving. This can be for a straight line, where the slope indicates how far up (positive slope) or down (negative slope) a line travels while also indicating how far across it travels. A tangent line to a curve is also known as a slope.