Answer:
Explanation:
The boundary line of the inequality 2x - 3y < 4 can be found by first converting it to an equation and then graphing it. To convert it to an equation, you set it equal to 4:
2x - 3y = 4
Now, to graph this line, you can find its x- and y-intercepts.
X-intercept:
Set y to 0 and solve for x:
2x - 3(0) = 4
2x = 4
x = 4/2
x = 2
So, the x-intercept is (2, 0).
Y-intercept:
Set x to 0 and solve for y:
2(0) - 3y = 4
-3y = 4
y = 4/(-3)
y ≈ -1.33 (rounded to two decimal places)
So, the y-intercept is (0, -1.33) or approximately (0, -4/3).
Now, you can plot these two points and draw a straight line through them. This line represents the boundary of the inequality 2x - 3y < 4.
The line will have a positive slope, passing through the points (2, 0) and (0, -1.33), and it will be shaded below this line to represent the region that satisfies the inequality 2x - 3y < 4.