Question

How do you write 5x – 3y < 6 in slope intercept form?

Answer 1

We will first take all the quantities except the quantities containing y in the right hand side and then arrange and modify so that we have only y in the left hand side.

Complete step-by-step answer:
We are given that we are required to write 5x – 3y < 6 in slope – intercept form.
We will first take the 5x from addition in the left hand side of the above expression to subtraction in the right hand side, then we will obtain the following equation:-
$\Rightarrow$- 3y < 6 – 5x
We will now multiply the whole equation in above line by a negative sign to obtain the following equation:-
$\Rightarrow$3y > - 6 + 5x
Now, we will divide the equation mentioned above by 3 on both the sides, we will then obtain the following equation:-
$\Rightarrow y > \dfrac{{ - 6 + 5x}}{2}$
Simplifying the right hand side, we will then obtain the following equation:-
$\Rightarrow y > - 3 + \dfrac{{5x}}{2}$
Now, we will re – arrange the terms in the right hand side of the above equation to obtain the following equation:-
$\Rightarrow y > \dfrac{{5x}}{2} - 3$

Thus, we have obtained the slope intercept form.

Note:
The students must note that slope intercept form a line is generally given by: y = mx + c, but here we have an inequality, so we will have slope intercept in the form y < mx + c or y > mx + c.
The students must also note that whenever we multiply an in – equality by a negative sign, the sign always changes from less than or less than equal to into greater than or greater than equal to respectively and vice – versa.
Slope intercept form helps us to form the graph easily as we can see the slope and intercept of both the equations very easily.