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

Solution:

The given inequality -6x + 2y ≤ 42 can be written in the equality form first as:

-6x + 2y = 42

The slope and intercept form of a linear equation is written as:

y = mx + c

Where m is the slope of the line and c is the intercept.

Therefore we can now write the slope intercept form of the given equation:

-6x + 2y = 42

Adding 6x to both sides

-6x + 6x + 2y = 42 + 6x

2y = 42 + 6x

Dividing by 2 throughout

2y/2 = 42/2 + 6x/2

y = 21 + 3x

Or

y = 3x + 21

Introducing back the inequality we can write

y ≤ 3x + 21

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

Summary:

Writing the inequality -6x + 2y ≤ 42 in the slope-intercept form we have y ≤ 3x + 21