Question

Write the following inequality in slope-intercept form. −6x + 2y ≤ 42

Answer 1

Add the 6x to both sides. Then divide both sides by 2 to get y by itself.

y <= 6x + 42

Note: if it were a -2y, you’d have to flip the inequality sign when dividing by that negative 2.

:)

Answer 2

Answer: The required slope-intercept form is
`y\leq 3x+21.`.

Step-by-step explanation: We are given to write the following inequality in slope-intercept form :

`-6x+2y\leq 42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know that

the slope-intercept form of an inequality of the given form is as follows :

`y\leq mx+c,` where m is the slope and c is the y-intercept.

From inequality (i), we have

`-6x+2y\leq 42\\\\\Rightarrow 2y\leq6x+42\\\\\Rightarrow y\leq(6)/(2)x+(42)/(2)\\\\\Rightarrow y\leq 3x+21.`

Thus, the required slope-intercept form is
`y\leq 3x+21.`.