Question

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

Answer 1

Hint: 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.