5.4.1 Finding the Equation of a Straight Line Using the
Slope - Intercept form of a line ( y =mx +b)
When asked to find the equation of a line using the slope-intercept
form ( y = mx + b) of the line, the goal is to find the constants m and b
(x and y remain as variables).
Steps to find the equation of a straight line
using the slope-intercept form of a line ( y =mx +b)
1. Substitute the given values for x , y and m into
y = mx + b and solve for the value of b.
2. Keep x and y as variables and substitute the now known values
for m and b into the equation y = mx + b.
Example 1
Find the equation of the line that has slope 3 and
passes through the point (0, 2).
Set m = _____, x = _____, and y = _____ in the equation
y = mx + b, and solve for b. Then write the equation in the form
y = mx + b.
Example 2
Find the equation of the line that has slope -1/2 and
passes through the point (-2, 4).
Set m = _____, x = _____, and y = _____ in the equation
y = mx + b, and solve for b. Then write the equation in the form
y = mx + b.
Example 3 Find the equation of the line that has
slope 2/3 and
passes through the point (3, -3).
Example 4 Find the equation of the line that has slope –3/2 and
passes through the point (4, - 2).
5.4.2 Finding the Equation of a line using the
Point-Slope
formula, 
Point-Slope Formula for a Line
The point-slope formula for a line is 
,
where the
line has slope m and passes through the point whose coordinates are
.
Example 1 Use the point-slope formula to find the equation of the
line that that passes through the point (-2, -1) and has
slope 3/2.
5.4.3 Finding the Equation of a line given two points
on
the line.
Example 2 Find the equation of the line that passes through the
points (-4, -5) and (8, 4).
Example 3 Find the equation of the line that passes
through the
points (-3, -9) and (1, -1).
Example 4
a. Find the equation of line 1.
b. Find the equation of line 2. |
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Skip section 5.5
5.6 Graphing Linear Inequalities in Two Variables
Linear Inequality in two Variables
A linear inequality in two variables is two ex pressions separated by
one of the inequality symbols (<, >, ≤, ≥)
Example 1
Graph y = x - 2 |
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Note The graph of y = x - 2 separates the
coordinate plane into
three disjoint sets of points:
|
1. On the Line: |
The set of points y = x - 2, which lie on the
line. |
| |
|
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2. Above the Line: |
The set of points y > x - 2, which lie
“above” the line. The region above the line
is called the upper half-plane. |
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|
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3. Be low the Line : |
The set of points y < x - 2, which lie
“below” the line. The region below the line
is called the lower half-plane. |
Steps to Graph an Inequality
1. Solve the inequality for y (isolate y).
2. Graph the line y = mx + b as a solid or dashed line as follows:
a. Draw a solid line if the inequality from step 1 is in the form
y≥ mx + b or y ≤ mx + b . A solid line indicates the line is part
of the solution set .
b. Draw a dashed line if the inequality from step 1 is in the form
y > mx + b or y < mx + b . A dashed line indicates the line is
just a boundary and is not part of the solution set.
3. Shade-in the upper half-plane or the lower half-plane as follows:
a. Shade-in the region above the line if the inequality from step 1
is in the form y > mx + b or y ≥ mx + b .
b. Shade-in the region below the line if the inequality from step 1
is in the form y < mx + b or y ≤ mx + b .
Example 2 Graph the solution set to 2x - 3y ≤6.
Example 3 Graph the solution set to 2x - 3y > 6.
Example 4
Graph the solution set to 3x + y > -2. |
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Example 5
Graph the solution set to x - 3y ≤ 2. |
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Example 6 Graph the solution set to (a) y > 3, and
(b) x ≤ 4.
Example 7 Write the inequality for each graph
shown.
