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Can you identify the slope and y-intercept of the graph? How does this help you write an inequality?
y≤-2/3x+1
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, 1) and (3,-1), 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=-2/3 ⇔ m= -2/3
One of the points we selected, (0, 1), 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= -2/3x+ 1
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 ? -2/3x+1 To figure out what the symbol should be, we need a test point that lies within the solution set.