Download Notes to go with Lesson 4-4 Example 1 (an extra example) Write an

Notes to go with Lesson 4-4
Example 1 (an extra example)
Write an equation in slope-intercept form for the line that passes through (4, -2) and is parallel to
Y=1/2x – 7
*Since they are asking for a line parallel to the line given, the equation must have the same slope as line
that was given. M = ½
*Use m = ½ and the point (4, -2) and plug into point-slope form.
Y – (-2) = ½ (x – 4)
Y + 2 = ½ x -2
-2
-2
Distribute
Solve for y, so the equation is in slope-intercept form.
Y=½x-4
Example 2
If the book shows you are picture, you are going to have to look at the slopes of the line to determine if
the lines are parallel (same slope) or perpendicular (negative reciprocals)
Example 3 (an extra example)
If the question asks you determine which lines are parallel or perpendicular, write all of the lines in
slope-intercept (solve for y) and look at the slopes. Don’t worry about graphing them!!!!
Determine whether the graphs of 3x + y = 12, y = 1/3 x + 2, and 2x – 6y = -5
3x + y = 12
-3x
y = 1/3 x + 2
-3x
-2x
Y = -3x + 12
m = -3
2x – 6y = -5
-2x
-6y = -2x - 5
-6
-6 -6
m = 1/3
y = 1/3x + 5/6
m = 1/3
Since y = 1/2x + 2 and 2x – 6y = -5 both have a slope of 1/3, they are parallel. 3x + y = 12 is
perpendicular to the other two equations because their slopes are negative reciprocals of each other.
Example 4 (an extra example)
Write an equation in slope-intercept form for the line that passes through (4, -2) and is perpendicular to
the graph of 7x – 2y = 3.
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You need to rewrite the equation in slope-intercept form, so that you can determine its slope.
7x – 2y = 3
-7x
-7x
(subtract 7x from both sides)
-2y = -7x + 3
-2 -2 -2
(divide everything by -2)
Y = 7/2x - 3/2 (slope-intercept form)
The slope of the line is 7/2.
Since the question asks about a perpendicular line, you need to use the negative reciprocal,
which is -2/7
Now, plug m =-2/7 and the point given (4, -2) into point-slope so you can begin to write the
equation.
Y – (-1) = -2/7(x – 4)
(Point-slope form)
Y + 1 = -2/7x + 8/7
(distribute -2/7)
-1
-1
(subtract 1 from both sides to solve for y)
Y = -2/7x + 1/7
The answer is -2/7x + 1/7
(8/7 =1 and 1/7. When you subtract 1, it equals 1/7)