1.2 Graphing Linear Inequalities in Slope-Intercept Form
Example 1: Solving Inequalities for y
`
Remember, when you multiple or divide by a negative number, you must change the direction of the
inequality sign
Solve for y
3 2 2
3
3
2 3 2
2 3 2
2
2
3
1
2
Solve each equation for y.
a) 2 4 2
b) 3 2
Example 2: Graphing a line in Slope-Intercept Form
When graphing a line in slope-intercept form, , follow the steps
1) Plot the y-intercept
2) Use the slope to find another point on the graph
a) Equations with positive slope
Graph the line given by the equation 2
Start at the y intercept which is the point 0, 2
Remember for positive slope
Next, follow the slope to the next point on the graph.
Since this is a positive slope, another point can be found
by moving either
• Up 3 units and right 4 units OR
• Down 3 units and left 4 units
point by moving:
•
•
Up a units, right b units OR
Down a units, left b units
The next points that we can find on the graph are 4,1 and 4, 5.
find a new
Sketch the graph of the function 1
b) Equations with a negative slope.
Sketch the graph of the equation 3
Start at the y-intercept which is the point 0,3.
Next, find another point on the graph by using the slope and moving either
• Down 2 units and 5 right OR
• Up 2 units and 5 left
The next points on the graph are 5, 1 and 5,5
Sketch the graph of the function 3 1
Remember, if the slope is an
integer, rewrite it as a
fraction over 1
EX: 2 1
The slope is
Example 3: Graphing a linear inequality in slope-intercept form
When graphing a linear inequality in slope-intercept form, the inequality sign indicates two things
1) Whether to shade above or below the line
2) Whether to use a solid line or dashed line.
For greater than or equal to, and less than or equal to the line should be a solid line because it includes all of the
values on the line. For less than and greater than, the line should be dotted because the points on the line are
not included in the solution.
For y greater than and greater than or equal to, shade above
the line
For y less that and less than or equal to, shade below the line.
For example, sketch the line 2 3 6
Solid Line
Dashed Line
Shade above
Shade Below
First, the equation needs to be written in slope-intercept form.
2 3 6
2
2
3 2 6
3 2
6
3
3 3
2
2
3
Since the inequality is less than and not less than or equal to, the line must be dashed.
Also, the equation is , so the graph should be shaded below
Assignment 1.2
Solve each inequality for y and write it in lope-intercept form. Leave your slope as a fraction if necessary.
1. 4 4
2. 3
3. 9 5 20
4. 2 5 4
5. 3 8 4
Sketch each inequality by first writing the equation in slope-intercept form. Label the coordinates of the y-intercept and
one other point on the graph.
6. 2 5 10
8. 15 5 5
7. 2 4 6
9. 6 3 9