Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
6. Graphing Linear Inequalities in Two Variables
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Exercise 44 Page 254

First find the equation of the boundary line.

Inequality: y ≤ 2x+1
Graph:

Practice makes perfect

Let's start by writing the equation of the boundary line. First we will calculate the slope using the given points.

m=y_2-y_1/x_2-x_1
m=-5- 5/- 3- 2
â–¼
Simplify right-hand side
m=-10/-5
m=2

Next we substitute the slope m= 2 and one of the points ( 2, 5) into the point-slope form and solve for y.

y-y_1=m(x-x_1)
y- 5= 2(x- 2)
â–¼
Solve for y
y-5=2x-2* 2
y-5=2x-4
y=2x+1

To find the inequality symbol we should use we graph the boundary line along with the remaining two points that are solutions.

To include (6,5) as a solution of the inequality we have to shade everything below the boundary line, which means we need to use the inequality symbol that signals less than, <. y<2x+1 The second point (- 2,- 3) lies on the boundary line, which means the boundary line has to be included in the solution set. The inequality symbol we are looking for is less than or equal to, ≤. Let's write our final inequality. y ≤ 2x+1 Now we can graph the inequality, including all of the points.