WEEK 3
1.Read chapter 3 (except section 3.5) of the Dugopolski text.
Complete the following assignment problems:
- Pages 197–198, problems 9, 16, 25 & 56
- Page 209, problems 29, 51, & 59
- Pages 219-220, problems 12, 21, 24 & 82
- Pages 240-241, problems 17, 19, 29 & 49
Pg 197 - 198
9. Slope
find the slope of each line.
(y2-y1)/(x2-x1)
= (2-0)/(0-(-3))
= 2/3
16. Slope
find the slope of each line.
(y2-y1)/(x2-x1)
(-2-1)/(2-(-3))
= -3/5
25. Slope Using Coordinates
Find the slope of the line that goes through each pair of points.
( - 2, 4 ), ( 5, 9 )
(y2-y1)/(x2-x1)
= (9-4)/(5-(-2))
= 5/7
56. Parallel and Perpendicular Lines
In each case, determine whether the lines and are parallel,
perpendicular, or neither.
Slope1 = (0-(-2))/(2-(-2)) = 2/4 = ½
Slope2 = (3-5)/(-1-(-2)) = -2/1 = -2
Since they are negative reciprocals, they are perpendicular.
Pg 209
29. Slope-Intercept Form
Find the slope and y-intercept for each line that has a slope
and y-intercept.
x + y = 5
Subtract x:
y = -x + 5
51. Standard Form
Write each equation in standard form using only integers.
Multiply by 10:
5x = 6y
Subtract 6y:
5x-6y = 0
59. Using Slope-Intercept Form for Graphing
Graph each line using its y-intercept and slope.
Pg 219 – 220
12. Point-Slope Form
Write each equation in slope-intercept form.
2x + 3y = 90
Subtract 2x:
3y = -2x + 90
Divide by 3:
y = -2/3 x + 30
21. Find the equation of the line that goes through the given point
and has the given slope. Write the answer in slope-intercept
form.
Point slope form:
y-y1 = m(x-x1)
y-5 = -1/2(x-(-2))
y-5 = -1/2 x – 1
Add 5:
y = -1/2 x + 4
24. ( - 1, - 5), - 8
y-y1 = m(x-x1)
y-(-5) = -8(x-(-1))
y+5 = -8x – 8
Subtract 5:
y = -8x - 13
82. Age at first marriage. The median age at first marriage for
females increased from 24.5 years in 1995 to 25.1 years in
2000 (U.S. Census Bureau, Let 1995 be
year 5 and 2000 be year 10.
a) Find the equation of the line through (5, 24.5) and
(10, 25.1).
get the slope:
(y2-y1)/(x2-x1)
(25.1-24.5)/(10-5)
= 0.12
Use point slope form:
y-y1 = m(x-x1)
y-25.1 = 0.12(x-10)
Distribute:
y-25.1 = 0.12x - 1.2
Add 25.1:
y = 0.12x + 23.9
b) What do x and y represent in your equation?
X is the number of years after 1990
Y is the age at first marriage
c) Interpret the slope of this line.
The slope is the increase in median age for each year that goes by.
d) In what year will the median age be 30?
30 = 0.12x + 23.9
Subtract 23.9:
0.12x = 6.1
Divide by 0.12:
X = 50.8333
Year 2040.83, so in the year 2040
e) Graph the equation.
Pg 240 – 241
17. Graphing a Linear Inequality
Graph each inequality.
y > - x + 3
19.
29.
49. The Test-Point Method
Graph each inequality using a test point.
x < 5y - 100
Try (0, 0)
0 < 0 – 100
0 < -100
False, so (0, 0) is not in the shaded area