then/now you used the properties of parallel lines to determine congruent angles. find slopes of...
TRANSCRIPT
You used the properties of parallel lines to determine congruent angles.
• Find slopes of lines.
• Use slope to identify parallel and perpendicular lines.
• slope
• rate of change
Find the Slope of a Line
A. Find the slope of the line.
Substitute (–3, 7) for (x1, y1) and (–1, –1) for (x2, y2).
Answer: –4
Slope formula
Substitution
Simplify.
Find the Slope of a Line
B. Find the slope of the line.
Substitute (0, 4) for (x1, y1) and
(0, –3) for (x2, y2).
Answer: The slope is undefined.
Slope formula
Substitution
Simplify.
Find the Slope of a Line
C. Find the slope of the line.
Answer:
Slope formula
Substitution
Simplify.
Substitute (–2, –5) for (x1, y1) and (6, 2) for (x2, y2).
Find the Slope of a Line
D. Find the slope of the line.
Answer: 0
Slope formula
Substitution
Simplify.
Substitute (–2, –1) for (x1, y1) and (6, –1) for (x2, y2).
A.
B.
C.
D.
A. Find the slope of the line.
A. 0
B. undefined
C. 7
D.
B. Find the slope of the line.
A.
B.
C. –2
D. 2
C. Find the slope of the line.
A. 0
B. undefined
C. 3
D.
D. Find the slope of the line.
Determine Line Relationships
Step 1 Find the slopes of and .
Determine whether and are parallel, perpendicular, or neither for F(1, –3), G(–2, –1), H(5, 0), and J(6, 3). Graph each line to verify your answer.
Determine Line Relationships
Step 2 Determine the relationship, if any, between the
lines.The slopes are not the same, so and are not parallel. The product of the slopes is
So, and are not
perpendicular.
Determine Line Relationships
Answer: The lines are neither parallel nor perpendicular.
Check When graphed, you can see that the lines are
not parallel and do not intersect in right angles.
A. parallel
B. perpendicular
C. neither
Determine whether AB and CD are parallel, perpendicular, or neither for A(–2, –1), B(4, 5), C(6, 1), and D(9, –2)
Use Slope to Graph a Line
First, find the slope of .
Slope formula
Substitution
Simplify.
Graph the line that contains Q(5, 1) and is parallel to MN with M(–2, 4) and N(2, 1).
Use Slope to Graph a Line
The slope of the line parallel to through Q(5, 1) is .
The slopes of two parallel lines are the same.
Graph the line.
Draw .
Start at (5, 1). Move up 3 units and then move left 4 units.
Label the point R.
Answer:
Graph the line that contains R(2, –1) and is parallelto OP with O(1, 6) and P(–3, 1).
A. B.
C. D. none of these