How do you write the inequality 6x + 2y < 42 in slope-intercept form?

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To rewrite the inequality 6x + 2y < 42 in slope-intercept form, follow these steps:

  1. Start with the original inequality:
  2. 6x + 2y < 42
  3. Isolate the term with the variable y on one side. First, subtract 6x from both sides:
  4. 2y < -6x + 42
  5. Next, divide every term in the inequality by 2 to solve for y:
  6. y < -3x + 21
  7. Now, you have the inequality in slope-intercept form, which is y < -3x + 21. Here, the slope is -3 and the y-intercept is 21.

This means that for any point (x, y) that lies below the line represented by y = -3x + 21, the inequality holds true.

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