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.