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 ≤ 70Step 2: Subtract 5x from Both Sides
To isolate the term involving y, we subtract 5x from both sides:
5y ≤ -5x + 70Step 3: Divide Everything by 5
Next, we divide every term by 5 in order to solve for y:
y ≤ -x + 14Final Result
The inequality in slope-intercept form is:
y ≤ -x + 14Here, 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.