3.4 Slope & Rate of Change DAY TWO with work
7
3.4 Slope & Rate of Change DAY TWO with work 1 OBJECTIVE 4: Slopes of Parallel & Perpendicular Lines DAY TWO Two lines in the same plane are parallel if they do not intersect. If the lines are not in the same plane they are considered skew . Parallel lines have the same steepness, slope, but have a different yintercept. Two lines are perpendicular if they lie in the same plane AND meet/ intersect at a 90 o , right angle.
Transcript of 3.4 Slope & Rate of Change DAY TWO with work
3.4 Slope & Rate of Change DAY TWO with work
1
OBJECTIVE 4: Slopes of Parallel & Perpendicular Lines
DAY TWO
Two lines in the same plane are parallel if they do not intersect. If the lines are not in the same plane they are considered skew.
Parallel lines have the same steepness, slope, but have a different yintercept.
Two lines are perpendicular if they lie in the same plane AND meet/intersect at a 90o, right angle.
3.4 Slope & Rate of Change DAY TWO with work
2
Example 8: Determine whether each pair of lines is , , or .a) b) c) x + y = 3
x + y = 4
3x + y = 5
2x + 3y = 6
parallel perpendicular neither
parallelperpendicular
neither
3.4 Slope & Rate of Change DAY TWO with work
3
Practice 8: Determine whether each pair of lines is , , or .a) b) c) x + y = 11
2x + y = 11
2x + 3y = 21
6y = 4x 2
y = 5x + 1
x 5y = 10
parallel perpendicular neither
perpendicularneither
parallel
3.4 Slope & Rate of Change DAY TWO with work
4
OBJECTIVE 5: Slope as a Rate of ChangeSlope tells us how fast y is changing with respect to x or because of x.
The pitch of the roof on the left is
The roof rises vertically 7 feet and runs horizontally 10 feet.
The grade of the road on the right is written as a %. A 7% grade, means that the road rises (or falls) 7 feet for every horizontal 100 feet.
rate of change =
Example 9: Finding the Grade of a RoadAt one part of the road to the summit of Pikes Peak, the road rises at a rate of 15 vertical feet for a horizontal distance of 250 feet. Find the grade of the road.
3.4 Slope & Rate of Change DAY TWO with work
5
Practice 9: One part of the Mt. Washing ton (New Hampshire) cog railway rises about 1794 feet over a horizontal distance of 7176 feet. Find the grade of this part of the railway.
Example 10: Finding the Slope of a LineThe following graph shows annual food and drink sales y (in billions of dollars) for year x.
a) Find the slope of the line and attach the proper units for the rate of change.
b) Then write a sentence explaining the meaning of the slope for this application. Interpret your answer from a.
3.4 Slope & Rate of Change DAY TWO with work
6
Practice 10: Finding the Slope of a LineThe following graph shows cost y (in dollars) of having laundry done at the WashnFold, where x is the number of pounds of laundry.
a) Find the slope of the line, and attach the proper units for the rate of change.
b) Then write a sentence explaining the meaning of the slope for this application. Interpret your answer from a.
3.4 Slope & Rate of Change DAY TWO with work
7
HW DAY TWO:
pg. 217: 41 89 (o), 91 107 (o)
