How can I rewrite the inequality 6x + 2y ≤ 46 in slope-intercept form?

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To rewrite the inequality 6x + 2y ≤ 46 in slope-intercept form, we need to isolate y on one side of the inequality. Slope-intercept form is typically structured as y = mx + b, where m represents the slope and b denotes the y-intercept.

Here are the detailed steps to perform the conversion:

  1. Start with the original inequality: 6x + 2y ≤ 46.
  2. To isolate 2y, subtract 6x from both sides:

    3. 2y ≤ -6x + 46

  3. Next, divide every term by 2 to solve for y:

    4. y ≤ -3x + 23

Now we have successfully rewritten the inequality in slope-intercept form: y ≤ -3x + 23.

In this form, you can clearly see that the slope (-3) indicates that for every unit increase in x, y decreases by 3. The y-intercept (23) shows the point at which the line crosses the y-axis.

Understanding this form allows you to easily graph the inequality, which can help visualize the solution set (the area beneath the line).

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