Download Post your 50-word response to the following: How can you

Post your 50-word response to the following: How can you determine if two
lines are perpendicular?
To determine if two lines are perpendicular, you need to look at their slopes. If the
slopes are negative reciprocals, they are perpendicular lines.
A. Find the slope and the y-intercept of the line.
10x = 7y + 63
Solve for y:
7y = 10x – 63
Divide by 7:
Y = 10/7 x – 9
Slope = 10/7
Y intercept = (0,-9)
B. Find the slope and y-intercept of the line. Write fractional answers in lowest
terms.
9y + 3x + = 20 + 3x
Is something missing here?
If not:
Subtract 3x:
9y = 20
Y = 20/9
Slope = 0
Y intercept = (0,20/9)
The slope is ___.
The y-intercept is (0, __)
C. Find the slope, if it exists, of the line containing the pair of points.
( 7,8) and ( 10,-8)
Slope = rise/run
= (-8-8)/(10-7)
= -16/3
The slope m = ___ ( simplify your answer. Type an integer or a fraction. Typed N
if the slope is undefined.)
D. Find the slope, if it exists, of the line containing the pair of points.
( -2,-7 ) and ( -20, -10)
Slope = rise/run
= (-10-(-7)) / (-20-(-2))
= -3/-18
= 1/6
The slope m __ ( simplify your answer. Type an integer or fraction. Typed N if
the slope is undefined.)
E. Determine whether graphs of the pair of lines are parallel.
x + 10 = y
y – x = -6
What is the slope of the line x + 10 = y
1
What is the slope of the line y – x = -6
Add x:
Y=x–6
Slope = 1
Are the graphs of the even equation parallel ? Yes , the slopes are the same
F. Find the slope –intercept equation of the line that has the given characteristics.
y = 6x + 8
Slope 6 and y-intercept (0,8) The slope-intercept equation is y = __.
G. Find the slope –intercept equation of the line that has the given characteristics.
y = 7.4x - 8
Slope 7.4 and y-intercept (0, -8)
The slope –intercept equation y = ___. ( Use integers or decimal for any
numbers in the expression.)
H. Find an equation of the line having the given slope and containing the given
point. m = 9, (2,1)
y-y1 = m(x-x1)
y-1 = 9(x-2)
y-1 = 9x – 18
y = 9x - 17
The equation of the line is y = ____. ( Simplify your answer. Use integers or
fraction for any numbers in the expression)
I. Find an equation of the line having the given slope and containing the given
points.
m = 2/3, (7,-8)
y-y1 = m(x-x1)
y – (-8) = 2/3 ( x – 7)
y + 8 = 2/3 x – 14/3
y = 2/3 x – 38/3
The equation of the line is y = ___. ( simplify your answer. Use integers or
fraction for any number in the expression.)
J. Find an equation of the line containing the given pair of points. Express your
answer in the form x = a, y = b, or y = mx + b.
(-8,-8) and (1,1)
Slope = rise/run
= (1-(-8))/(1-(-8))
=1
y-y1 = m(x-x1)
y-1 = x-1
y=x
What is an equation of the line ? y = __. ( Simplify your answer)
K. Find an equation of the line containing the given pair of points.
( -2,-5) and (-8,-7)
Slope = rise/run
(-7 – (-5)) / (-8 – (-2))
= -2/-6
= 1/3
y-y1 = m(x-x1)
y-(-5) = 1/3 (x-(-2))
y+5 = 1/3 (x + 2)
y + 5 = 1/3 x + 2/3
y = 1/3 x – 13/3
The equation of the line is y = ___. ( Simplify your answer. Use integers or
fractions for any numbers in the expression.)
L. Find an equation of the line containing the given pair of points.
( 1/6, -1/3) and ( 5/8, 3)
Slope = rise/run
= (3-(-1/3))/(5/8 – 1/6)
= 80/11
y-y1 = m(x-x1)
y – 3 = 80/11(x-5/8)
y – 3 = 80/11 x – 50/11
y = 80/11 x – 17/11
What is the equation of the line ? y = ___ ( Simplify your answer. Typed answer
in the form y = mx + b using integer or fraction.)
M. Write an equation of the line containing the given point and parallel to the
given line. Express your answer in the form y = mx + b.
(8, 9); x + 7y = 6
7y = -x + 6
Y = -(1/7)x + 6/7
Slope = -1/7
y-y1 = m(x-x1)
y-9 = -1/7(x-8)
y-9 = -1/7 x + 8/7
y = -1/7 x + 71/7
The equation of the line is y = ____. ( Simplify your answer. Use integers or
fraction for any numbers in the expression.)
N. Write an equation of the line containing the given point and parallel to the
given line. Express your answer in the form y = mx + b.
( -7,4); 2x = 9y + 5
Solve for y:
9y = 2x – 5
Y = (2/9)x – 5/9
y-y1 = m(x-x1)
y-4 = 2/9(x – (-7))
y-4 = 2/9(x+7)
y-4 = 2/9 x + 14/9
y = 2/9 x + 50/9
The equation of the line is y = ___. ( Simplify your answer. Use integers or
fraction for any numbers in the expression.)
O. Write an equation of the line containing the given point and perpendicular to
the given line. Express your answer in the form y = mx + b
(7,9); 6x + y = 8
Y = -6x + 8
Negative reciprocal of the slope
= 1/6
y-y1 = m(x-x1)
y-9 = 1/6(x-7)
y-9 = 1/6 x – 7/6
y = 1/6 x + 47/6
The equation of the line is y = ____. ( Simplify your answer. Use integer or
fraction for any numbers in the expression.)
P. Write an equation of the line containing the given point and perpendicular to
the given line.
( 8,-4 ); 4x + 7y = 2
7y = -4x + 2
Y = (-4/7)x + 2/7
Negative reciprocal = 7/4
y-y1 = m(x-x1)
y-(-4) = 7/4 (x-8)
y + 4 = 7/4 x – 14
y = 7/4 x - 18
The equation of the line is y = ____. ( Typed your answer in the form y = mx + b.
Simplify your answer. Typed an integer or a fraction.)
Q. The table lists data regarding the average salaries of several professional
athletes in the years 1991 and 2001.
1. Use the data points to find a linear function that fits the data.
2. Use the function to predict the average salary in 2005 and 2010.
Year
Average Salary
1991
$255,000
2001
$1,430,000
A linear function that fits the data is S(x) = ___. ( Let x = the number of years since
1990, and let S = the average salary x years from 1990. )
So 1991 means x = 1
2001 means x = 11
Slope = rise/run
= (1430000-255000)/(11-1)
= 117500
y-y1 = m(x-x1)
y-255000 = 117500(x-1)
y-255000 = 117500x – 117500
S(x) = 117500x + 137500
The predicted average salary for 2005 is $ ___. ( Round to the nearest whole number. )
S = 15
S(15) = 1900000
The predicted average salary for 2010 is $ ___. ( Round to the nearest whole number. )
S = 20
S(20) = 2487500
R. In 1920, the record for a certain race was 45.6 sec. In 1980, it was 45.0 sec. Let R(t) =
the record in the race and t = the number of years since 1920.
1) Find a linear function that fits the data.
2) Use the function in (a) to predict the record in 2003 and in 2006.
3) Find the year when the record will be 44.7 sec.
Find a linear function that fits the data. R(t) = __. ( Round to the nearest hundredth.)
Slope = rise/run
= (45-45.6)/(60-0)
= -0.01
R(t) = -0.01t + 45.6
What is the predicted record for 2003 ? ___ sec ( Round to the nearest tenth. )
R(83) = -0.01*83 + 45.6
= 44.77 sec
What is the predicted record for 2006 ? ___sec. ( Round to the nearest tenth. )
R(86) = -0.01*86 + 45.6
= 44.74 sec
In what year will the predicted record be 44.7 seconds ? ( Rounds to the nearest year, )
Set R = 44.7:
44.7 = -0.01t + 45.6
Subtract 45.6:
-0.9 = -0.01t
Divide by -0.01:
T = 90 years after 1920
Year 2010
S. In 1991, the life expectancy of males in a certain country was 73.1 years. In 1995, it
was 76.6 years. Let E represent the life expectancy in year t and let t represent the
number of years since 1991.
The linear function E(t) that the data is E(t) = ___t + ___. ( Round to the nearest tenth)
Slope = rise/run
= (76.6-73.1)/(1995-1991)
= 0.875
E(t) = 0.875t + 73.1
Use the fraction to predict the life expectancy of males in 2003.
E(12) = _____ ( Round to the nearest tenth.)
E(12) = 0.875*12 + 73.1
E(12) = 83.6 years