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Graphs to Linear Inequalities
In this topic, you will find the inequality based on its graph.
To find the ineqaulity, follow these steps:
Example 1:
Write the inequality that represents this graph. Examples: y>3x/4, x<=2, y>=1, y>-2x Inequality: Step 1: Find the equation of the boundary line. The boundary line is vertical. Its equation is x = -1. Step 2: Choose a point (x, y) on the shaded side of the line. Let's pick (-3, 0) on the shaded side. Step 3: Plug x and y into the bounday line equation to determine the inequality sign. x?-1 -3?-1Plug in (-3,0) -3<-1"Less than" makes the inequality true x<-1Boundary line is dashed
Step 2: Choose a point (x, y) on the shaded side of the line. Let's pick (-3, 0) on the shaded side.
Step 3: Plug x and y into the bounday line equation to determine the inequality sign.
Example 2:
Write the inequality in y=mx+b format. Examples: y>2x-3, y<=-4x/3+1 Inequality: Step 1: Find the equation of the boundary line. The slope of the line is -5/4 and the y-intercept is 3. So the equation of the boundary line is y = -54 x + 3. Step 2: Choose a point (x, y) on the shaded side of the line. Let's pick (5, 0) on the shaded side. Step 3: Plug x and y into the bounday line equation to determine the inequality sign. y ? -54 x + 3 0 ? -54 (5) + 3 Plug in (5, 0) 0 > -134 "Greater than" to make the inequality true y ≥ -54 x + 3 Boundary line is solid
Step 2: Choose a point (x, y) on the shaded side of the line. Let's pick (5, 0) on the shaded side.
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