Question

How do you write the linear equation \[5x - 3y = 24\] in slope-intercept form?

Answer 1

Hint: Here we will firstly write the actual standard form of the slope intercept form. Then we will modify our given linear equation to get it in the standard form of the slope intercept form.

Complete Step by Step Solution:
Given linear equation is \[5x - 3y = 24\]
We know that the slope-intercept form of a linear equation can be represented in the standard form i.e. \[y = mx + c\] where, \[m\] is the slope of the line and \[c\] is the y-intercept value.
Now we will modify the given linear equation and form it in the form of the standard slope intercept form.
So, we will keep the term which has the variable y on one side of the equation and all the remaining terms on the other side of the equation. Therefore, we get
\[ \Rightarrow 3y = 5x - 24\]
Now we will simply divide the both sides of the equation by 3 to get the required equation. Therefore, we get
\[ \Rightarrow \dfrac{{3y}}{3} = \dfrac{{5x - 24}}{3}\]
Now we will simplify the equation, we get
\[ \Rightarrow y = \dfrac{{5x}}{3} - \dfrac{{24}}{3}\]
\[ \Rightarrow y = \dfrac{{5x}}{3} - 8\]

Hence the linear equation \[5x - 3y = 24\] in slope-intercept form is written as \[y = \dfrac{{5x}}{3} - 8\].

Note:
Here we have to note that slope of a line is used to represent the orientation of the line i.e. how the line is inclined with the axis. We should remember that also the lines are said to be parallel if the slope of the lines are the same. For example let three lines A, B and C be the parallel lines then the slope of the line A must be equal to the slope of the line B which must be equal to the slope of the line C. the concept of the slope can also be used to check the co-linearity of the points in the space. For example let three points A,B and C be the collinear points then the slope of the line AB must be equal to the slope of the line BC must be equal to the slope of the line AC.