Question

How do you write \[3x - 2y = 5\] into slope intercept form?

Answer 1

Hint: Given is an equation with two variables x and y. but it is not in standard slope intercept form of a line. We know that standard slope intercept form is \[y = mx + c\] where m is the slope. Thus using the rearrangements and transpositions in the equation given we will convert it into standard form. It mainly needs the coefficient of \[y\] to be a compulsory one.

Complete step by step solution:
Given that \[3x - 2y = 5\]
Now first we will remove x terms from right side, so we will subtract \[3x\] from both sides
 \[3x - 2y - 3x = 5 - 3x\]
Now on LHS x term will be cancelled,
 \[ - 2y = 5 - 3x\]
Multiply both sides by -1.
 \[2y = - 5 + 3x\]
Only the signs of the terms are inverted.
Now rearrange the terms in standard form
 \[2y = 3x - 5\]
Now in order to make the coefficient of y equals to one divide both sides by 2,
 \[\dfrac{{2y}}{2} = \dfrac{{3x - 5}}{2}\]
On LHS we can cancel 2, whereas on RHS separate the terms
 \[y = \dfrac{{3x}}{2} - \dfrac{5}{2}\]
This is our standard slope intercept form \[y = mx + c\] .
So, the correct answer is “ \[y = \dfrac{{3x}}{2} - \dfrac{5}{2}\] ”.

Note: Note that writing the given equation in slope intercept form is simply a procedure of steps to be followed. That equation involves slope and intercept. That’s it!
Slope is the ratio of vertical change to horizontal change. If the line is increasing then slope is positive and if line is decreasing then slope is negative. Also note that in geometrical cases the slope is given with the help of tan function.