Let's start by graphing the given inequality. To do so, we must first identify the boundary line. To obtain the boundary line, we replace the inequality sign with an equals sign.
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Inequality & & Boundary Line
y< 5x+1 & & y= 5x+1
Since the line is already written in slope-intercept form, we will use its slope 5 and its y-intercept 1 to graph it. Note that the inequality is strict. Therefore, the line will be dashed.
Now that we have graphed the boundary line, we will determine the half-plane to shade. To do so, we will test a point. If substituting the point into the inequality produces a true statement, we will shade the region that contains the point. Otherwise, we will shade the opposite region. For simplicity, we will test the point (0,0).
Since the test point produced a true statement, we will shade the half-plane that contains (0,0).
Note that the solution set contains all the points that are below the line, without including the boundary line. Therefore, the region of the coordinate plane not included in the graph is the region above or on the line. This can be expressed by reversing the inequality sign, and making the inequality nonstrict.
y ≥ 5x+1
Let's see how the graph of this inequality looks like.
