To find the points on the boundary line of the inequality 15x + 2 < -15y + 2, we need to first rewrite the inequality in slope-intercept form, which is y = mx + b.
Let's start by isolating y on one side of the inequality:
15x + 2 < -15y + 2
15x < -15y
Divide both sides by -15 (remember to flip the inequality sign when dividing by a negative number):
x > y
Now we have the equation in slope-intercept form: y = -x.
To find the points on the boundary line, we can choose any x-value and substitute it into the equation to find the corresponding y-value. Let's choose two x-values and calculate the corresponding y-values:
For x = 0:
y = -(0)
y = 0
So one point on the boundary line is (0, 0).
For x = 1:
y = -(1)
y = -1
Another point on the boundary line is (1, -1).
Therefore, two points on the boundary line of the inequality 15x + 2 < -15y + 2 are (0, 0) and (1, -1).