3-3 slopes of lines you used the properties of parallel lines to determine congruent angles. find...
TRANSCRIPT
3-3 Slopes of Lines
You used the properties of parallel lines to determine congruent angles.
• Find slopes of lines.
• Use slope to identify parallel and perpendicular lines.
The Slope-Intercept Equation
y = mx + b
slopey-intercept
Create an equation of a line with a slope of -3 and a y-intercept of 4. y = -3x + 4
y = 4 – 3x3x = 4 - y-4 = -y – 3x
The Slope-Intercept Equation Example 1
y = mx + bCreate an equation of a line with a slope of -3 and a y-intercept of 4.
y = -3x + 4
Example 2Write an equation for the line with slope 3 that contains the point (-2,4)
y = mx + b
4 = 3 (-2) + b4 = -6 + b
+6 +610 = b
y = 3x + 10
substitute
solve for b
simplify
Example 2Write an equation for the line containing the points (1,5) and (2,8).
change in y-coordinatesm
change in x-coordinates
2 1
2 1
y ym
x x
8 5m
2 1
3m 3
1
Example 3Write an equation for the line containing the points (1,5) and (2,8).
m 3
y = mx + b
5 = 3 (1) + b5 = 3 + b
-3 -32 = b
y = 3x + 2
substitute
simplify
Find the Slope of a Line
C. Find the slope of the line.
Slope formula
Substitution
Simplify.
Substitute (–2, –5) for (x1, y1) and (6, 2) for (x2, y2).
Answer:
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. 0
B. undefined
C. 3
D.
D. Find the slope of the line.
Page 189
Page 189
RECREATION In 2000, the annual sales for one manufacturer of camping equipment was $48.9 million. In 2005, the annual sales were $85.9 million. If sales increase at the same rate, what will be the total sales in 2015?UnderstandUse the data given to graph the line that models the annual sales y as a function of the years x since 2000. The sales increase is constant. Plot the points (0, 48.9) and (5, 85.9) and draw a line through them.
You want to find the sales in 2015.
PlanFind the slope of the line. Use this rate of change to find the amount of sales in 2015.SolveUse the slope formula to find the slope of the line.
The sales increased at an average of $7.4 million per year.
Use the slope of the line and one known point on the line to calculate the sales y when the years x since 2000 is 15.
Slope formula
m = 7.4, x1 = 0, y1 = 48.9, x2 = 15Simplify.
Multiply each side by 15.
Add 48.9 to each side.
Answer: Thus, the sales in 2015 will be about $159.9 million.
Page 191
Parallel LinesParallel lines are lines in the same plane that never intersect.
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
Parallel lines have the same slope.
Perpendicular LinesPerpendicular lines are lines that intersect to form a 900 angle.
-8 -6 -4 -2
2
42 6 8
4
6
-4
-6
-8
-2
8
The product of the slopes of perpendicular lines is -1.
4m 2
2
2 1m
4 2
Determine whether these lines are perpendicular.
and y = -3x - 21
y x 73
1m
3 m = -3
13
3 1
Since the product of the slopes is -1, the lines are perpendicular.
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.
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.
3-3 Assignmentp. 193, 12-38 even, skip 26