Sign In
Can we identify the slope and the y-intercept of the graph? How does this help us write an inequality?
y<1/2x-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've identified two points, (0, -1) 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=1/2 ⇔ m= 1/2 One of the points we selected, (0, -1), is also the y-intercept. 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= 1/2x+( -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 ? 1/2x-1 To figure out what the symbol should be, we need a test point that lies within the solution set.
x= 2, y= -2
Multiply
Subtract term