Algebra I Regents Review - Linear Inequalities
Regents Review Lesson #5: Graphing Linear Inequalities (and Systems)
Homework: See board/website
Warm Up
(Modeled from #20 on the August 2015 Regents)
If Joseph completes the square for g(x) = x2 - 10x + 3 in order to find the
minimum, he must write g(x) in the general form g(x) = (x - a)2 + b. What is the
value of a for g(x)?
(1) 5
(3) 10
(2) -5
(4) -10
Summary of Linear Inequalities
The solution of a linear inequality is any ordered pair that makes inequality true
y = 2x - 3
Solutions are points ON the line
y > 2x - 3
Solutions are coordinates in the
half-plane (shaded region)
Solutions may be on the line if ≤ or ≥
Algebra I Regents Review - Linear Inequalities
Summary of Linear Inequalities
Steps for Graphing Linear Inequalities
1) Solve inequality for y (get into slope-intercept form). Flip the sign if you
multiply/divide by a negative number
2) Graph the boundary line (Use slope and y-int)
• Use dashed line if inequality is < or >
• Use solid line if inequality is ≤ or ≥
3) Shade:
• ABOVE line for
• BELOW line for
or
or
4) Check that graph is shaded correctly by using a test point
Visual Representation of Linear Inequalities
Written as:
y ≥ or y >
Shade ABOVE!
Written as y ≥ or y ≤
line is SOLID
Written as y < or y
line is DASHED
Written as
y≤
Shade BELOW!
or
>
y<
Algebra I Regents Review - Linear Inequalities
Systems of Linear Inequalities
1. Graph together on same axes
2. Solution points must satisfy BOTH
inequalities (or lay in the double-shaded
region)
3. Label your lines!
Hints:
1) For word problems, look for key words to
generate symbols (see right)
2) Some word problems may be more easily
graphed using x and y- intercepts rather
than slope and y-intercept
Ex: 50x + 500y ≥ 2500
at least, minimum
≥
at most, maximum
≤
Skill Practice
1) Sketch the graph of -2y + x ≥ -8. Is the point (-1, 4) in the solution set?
Explain based on your graph.
2) Write the linear inequality graphed below:
Algebra I Regents Review - Linear Inequalities
Sample Regents Question
1)
Sample Regents Question
2)
Algebra I Regents Review - Linear Inequalities
Sample Regents Question
3)
Sample Regents Question
4)
Mr. W is having a yard sale, where he is selling iPad chargers and wireless keyboards. At the
end of the day, he knows he sold a maximum of 14 items, and he earned a total of $342. If he
charged $18 for each iPad charger (x) and $38 for each keyboard (y), write a system of
inequalities that models this situation.
b) Graph that system of inequalities
c) Is it possible that he sold 11 iPad charges and 3 wireless
keyboards? Explain based on your graph.
Algebra I Regents Review - Linear Inequalities
Summary
In your Regents notebook, write down the 3 most important things to remember
from this lesson
- These can be strategies, tips, things to watch out for, etc..
Exit Slip
Which point lies in the solution set of the system of inequalities
below?
2x + 3y > 9
-x - y ≥ - 6
(a) (9, -3)
(c) (3, 2)
(b) (6, 1)
(d) (-3, 4)