When you write 4x-6y is greater than or equal to 16 in slope-intercept form,is the answer y is less than or equal to 2/3x + 8/3?
4x-6y>=16
-6y>=16-4y
y<=4/6 y -16/6
yes, correct.
thanks
To check if the answer y is less than or equal to 2/3x + 8/3 is correct, we need to convert the inequality 4x - 6y ≥ 16 into slope-intercept form.
The slope-intercept form equation is given by: y = mx + b, where m represents the slope of the line and b represents the y-intercept.
To convert the given inequality into slope-intercept form, we'll follow these steps:
Step 1: Move the variable term to the other side of the inequality sign:
4x - 6y ≥ 16
Add 6y to both sides:
4x ≥ 6y + 16
Step 2: Rewrite the inequality in the form y ≥ mx + b:
To get the inequality in the form y ≥ mx + b, we need to divide the entire inequality by -6. However, since we are dividing by a negative number, the inequality sign will be reversed. So, instead of ≥, it becomes ≤.
Divide both sides of the inequality by -6:
(4x) / (-6) ≤ (6y + 16) / (-6)
Simplifying:
-(2/3)x ≤ -y - 8/3
Step 3: Rearrange the inequality to have "y" isolated:
Since we want the y-variable to be positive, multiply both sides by -1:
(2/3)x ≥ y + 8/3
Now the equation is in the form y ≤ (2/3)x + 8/3, not y ≥ (2/3)x + 8/3 as proposed in the question.
Therefore, the answer "y is less than or equal to 2/3x + 8/3" is incorrect. The correct answer in slope-intercept form is "y ≥ (2/3)x + 8/3."