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Can you identify the slope and y-intercept of the graph? How does this help you write an inequality?
y>3/2x-3
There are two major steps to writing an inequality when given its graph.
Let's get started by focusing on the boundary line.
Here we have identified two points, (0, -3) and (2,0), and indicated the horizontal and vertical changes between them. This gives us the rise
and run
of the graph, which will give us the slope m.
rise/run=3/2 ⇔ m= 3/2
One of the points we selected, (0, -3), is also the y-intercept, which is great news! This means that we can combine the slope m and the y-intercept at the point (0, b) to write an equation for the boundary line in slope-intercept form.
y= mx+ b ⇒ y= 3/2x+( -3)
To finish forming the inequality, we need to determine the inequality symbol. This means replacing the equals sign with a blank space, since it is still unknown to us. y ? 3/2x-3 To figure out what the symbol should be, we need a test point that lies within the solution set.