How can I rewrite the inequality 5x + 5y ≤ 70 in slope-intercept form?

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Rewriting the Inequality in Slope-Intercept Form

To convert the inequality 5x + 5y ≤ 70 into slope-intercept form, we need to isolate y on one side of the inequality. The slope-intercept form is typically expressed as y = mx + b, where m is the slope and b is the y-intercept.

Step 1: Start with the Original Inequality

We begin with:

5x + 5y ≤ 70

Step 2: Subtract 5x from Both Sides

To isolate the term involving y, we subtract 5x from both sides:

5y ≤ -5x + 70

Step 3: Divide Everything by 5

Next, we divide every term by 5 in order to solve for y:

y ≤ -x + 14

Final Result

The inequality in slope-intercept form is:

y ≤ -x + 14

Here, the slope (m) is -1 and the y-intercept (b) is 14.

Understanding the Result

This means that for any given value of x, the corresponding value of y must be less than or equal to the result of -x + 14. Graphically, this inequality represents all the points on or below the line defined by the equation y = -x + 14.

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