Question

How do you write $y + \dfrac{1}{3}x = 4$ into slope intercept form?

Answer 1

Here we will write the given equation in slope intercept form. Firstly we will write the slope intercept form for a general equation. Then we will subtract and add numbers or variables in the given equation as per our requirement to get our equation in slope intercept form. A slope is defined as the rate of change in $x$ divided by rate of change in $y$.

Complete step by step solution:
The general equation of slope intercept form of a line is given as $y = mx + b$.
For writing the given equation in the above form we will take all $y$ variables on one side.
For that, we will subtract $\dfrac{1}{3}x$ on both sides of the equation and get,
$\begin{array}{l} \Rightarrow y + \dfrac{1}{3}x - \dfrac{1}{3}x = - \dfrac{1}{3}x + 4\\\ \Rightarrow y = - \dfrac{1}{3}x + 4\end{array}$

So we get the intercept form the given equation as,
$y = - \dfrac{1}{3}x + 4$

Note:
A Line is a one-dimensional figure that extends endlessly in both directions. It is also described as the shortest distance between any two points. There are many ways to form a line depending on the nature of the equation such as Point-slope Form, Intercept Form, Determinant Form and many others. The Form we are using depends on the data we have. Intercept form is a specific form of linear equation in which we can write the equation in $y = mx + b$ form, where $m$ is the slope and $b$ is its $y$-intercept. This type of form is based on the intercept with both axes of the line. This form is very useful in determining the slope of the equation and also the $y$-coordinates which use the $y$-intercept $b$ in the equation.