![Page 1: Graphing a Linear Inequality Example 2 Graph 3.3. 2x2xy>– STEP 1 Change > to and write the equation in slope-intercept form. = 32x2xy = – Replace > with](https://reader036.vdocuments.site/reader036/viewer/2022082723/5a4d1b287f8b9ab059997e3c/html5/thumbnails/1.jpg)
Graphing a Linear InequalityExample 2
Graph 3.2xy >–
STEP 1 Change > to and write the equation in slope-intercept form.
=
32xy =– Replace > with = sign.
Graph the line with slope 2 and y-intercept 3. Because the inequality symbol is >, use a dashed line.
2x= + 3 Add 2x to each side. y
![Page 2: Graphing a Linear Inequality Example 2 Graph 3.3. 2x2xy>– STEP 1 Change > to and write the equation in slope-intercept form. = 32x2xy = – Replace > with](https://reader036.vdocuments.site/reader036/viewer/2022082723/5a4d1b287f8b9ab059997e3c/html5/thumbnails/2.jpg)
Graphing a Linear InequalityExample 2
STEP 2 Test the point . Substitute the point into the original inequality.
32x y >–
( )0, 0
STEP 3 Shade the half-plane that does not contain .( )0, 0
320 – ( )0?>
30 is not a solution.( )0, 0>
![Page 3: Graphing a Linear Inequality Example 2 Graph 3.3. 2x2xy>– STEP 1 Change > to and write the equation in slope-intercept form. = 32x2xy = – Replace > with](https://reader036.vdocuments.site/reader036/viewer/2022082723/5a4d1b287f8b9ab059997e3c/html5/thumbnails/3.jpg)
Writing a Linear InequalityExample 3
You can spend at most $40 on art supplies. Tubes of paint cost $6 each and brushes cost $4 each. Write an inequality to model the situation.
ART SUPPLIES
SOLUTION
Use a verbal model to write the inequality. Letx represent the number of tubes of paint and lety represent the number of brushes.
6 • x + 4 • y ≤ 40
![Page 4: Graphing a Linear Inequality Example 2 Graph 3.3. 2x2xy>– STEP 1 Change > to and write the equation in slope-intercept form. = 32x2xy = – Replace > with](https://reader036.vdocuments.site/reader036/viewer/2022082723/5a4d1b287f8b9ab059997e3c/html5/thumbnails/4.jpg)
Writing a Linear InequalityExample 3
ANSWERThe inequality 404y6x ≤+ models the situation.
![Page 5: Graphing a Linear Inequality Example 2 Graph 3.3. 2x2xy>– STEP 1 Change > to and write the equation in slope-intercept form. = 32x2xy = – Replace > with](https://reader036.vdocuments.site/reader036/viewer/2022082723/5a4d1b287f8b9ab059997e3c/html5/thumbnails/5.jpg)
Using the Graph of a Linear InequalityExample 4
Graph the inequality in Example 3. How many tubes of paint and how many brushes can you buy?
STEP 1 Change ≤ to and write the equation inslope-intercept form:
=
SOLUTION
10.y += –23 x
Graph the equation usinga solid line.
![Page 6: Graphing a Linear Inequality Example 2 Graph 3.3. 2x2xy>– STEP 1 Change > to and write the equation in slope-intercept form. = 32x2xy = – Replace > with](https://reader036.vdocuments.site/reader036/viewer/2022082723/5a4d1b287f8b9ab059997e3c/html5/thumbnails/6.jpg)
Using the Graph of a Linear InequalityExample 4
STEP 2 Test the point ( ): 0, 0 6( )0 + 4( )0?≤ 40
≤ 400
STEP 3 Shade the half-plane that contains( ).0, 0
ANSWER
Many solutions are possible, such as and You could buy 4 tubes of paint and 4 brushes or 2 tubes of paint and 5 brushes.
( )4, 4 ( ).2, 5
![Page 7: Graphing a Linear Inequality Example 2 Graph 3.3. 2x2xy>– STEP 1 Change > to and write the equation in slope-intercept form. = 32x2xy = – Replace > with](https://reader036.vdocuments.site/reader036/viewer/2022082723/5a4d1b287f8b9ab059997e3c/html5/thumbnails/7.jpg)
Guided Practice for Examples 2, 3, and 4
5. 1xy +<
Graph the inequality.
ANSWER
![Page 8: Graphing a Linear Inequality Example 2 Graph 3.3. 2x2xy>– STEP 1 Change > to and write the equation in slope-intercept form. = 32x2xy = – Replace > with](https://reader036.vdocuments.site/reader036/viewer/2022082723/5a4d1b287f8b9ab059997e3c/html5/thumbnails/8.jpg)
Guided Practice for Examples 2, 3, and 4
Graph the inequality.6. 3y3x ≥+
ANSWER
![Page 9: Graphing a Linear Inequality Example 2 Graph 3.3. 2x2xy>– STEP 1 Change > to and write the equation in slope-intercept form. = 32x2xy = – Replace > with](https://reader036.vdocuments.site/reader036/viewer/2022082723/5a4d1b287f8b9ab059997e3c/html5/thumbnails/9.jpg)
Guided Practice for Examples 2, 3, and 4
Graph the inequality.7. x – 12y ≤ –
ANSWER
![Page 10: Graphing a Linear Inequality Example 2 Graph 3.3. 2x2xy>– STEP 1 Change > to and write the equation in slope-intercept form. = 32x2xy = – Replace > with](https://reader036.vdocuments.site/reader036/viewer/2022082723/5a4d1b287f8b9ab059997e3c/html5/thumbnails/10.jpg)
Guided Practice for Examples 2, 3, and 4
Graph the inequality.8. y > 2–
ANSWER
![Page 11: Graphing a Linear Inequality Example 2 Graph 3.3. 2x2xy>– STEP 1 Change > to and write the equation in slope-intercept form. = 32x2xy = – Replace > with](https://reader036.vdocuments.site/reader036/viewer/2022082723/5a4d1b287f8b9ab059997e3c/html5/thumbnails/11.jpg)
Guided Practice
9. WHAT IF? In Example 3, suppose you can spend at most $36. Write and graph an inequality to model the situation. Find two possible solutions.
for Examples 2, 3, and 4
ANSWER36;4y6x ≤+
Sample answer: 6 tubes of paint and 0 brushes, or 0 tubes of paint and 9 brushes.