Given the inequality:
y + 5 < 6x + 2
Let's graph the inequality.
Apply the slope intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
Rewrite the inequality for y.
Subtract 5 from both sides of the inequality:
y + 5 - 5 < 6x + 2 - 5
y < 6x - 3
The inequality in slope-intercept form is:
y < 6x - 3
Let's create two points from the inequality.
The slope is = 6
At the y-intercept, the x-coordinate is 0.
Thus, the y-intercept is:
(0, -3)
When x = 0.5
y < 6(0.5) - 3
y < 3 - 3
y < 0
Thus, we have the points:
(x, y) ==> (0, -3), (0.5, 0)
Plot the points and connect them using dotted lines
Since y is less than 6x + 2, after plotting the graph we are to shade the area below the boundary line.
Thus, we have the graph below: