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

$-6x+2y\leq 42\\\\\Rightarrow 2y\leq6x+42\\\\\Rightarrow y\leq\dfrac{6}{2}x+\dfrac{42}{2}\\\\\Rightarrow y\leq 3x+21.$

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