<< Chapter < Page Chapter >> Page >

x + 2 4 x 1 3 = 2

x = −14

Got questions? Get instant answers now!

For the following exercises, solve each rational equation for x . State all x -values that are excluded from the solution set.

2 3 x + 4 = x + 2 x + 4

x −4 ; x = −3

Got questions? Get instant answers now!

3 x 2 = 1 x 1 + 7 ( x 1 ) ( x 2 )

Got questions? Get instant answers now!

3 x x 1 + 2 = 3 x 1

x 1 ; when we solve this we get x = 1 , which is excluded, therefore NO solution

Got questions? Get instant answers now!

5 x + 1 + 1 x 3 = 6 x 2 2 x 3

Got questions? Get instant answers now!

1 x = 1 5 + 3 2 x

x 0 ; x = −5 2

Got questions? Get instant answers now!

For the following exercises, find the equation of the line using the point-slope formula.

Write all the final equations using the slope-intercept form.

( 0 , 3 ) with a slope of 2 3

Got questions? Get instant answers now!

( 1 , 2 ) with a slope of 4 5

y = 4 5 x + 14 5

Got questions? Get instant answers now!

x -intercept is 1, and ( −2 , 6 )

Got questions? Get instant answers now!

y -intercept is 2, and ( 4 , −1 )

y = 3 4 x + 2

Got questions? Get instant answers now!

( −3 , 10 ) and ( 5 , −6 )

Got questions? Get instant answers now!

( 1 , 3 )   and   ( 5 , 5 )

y = 1 2 x + 5 2

Got questions? Get instant answers now!

parallel to y = 2 x + 5 and passes through the point ( 4 , 3 )

Got questions? Get instant answers now!

perpendicular to 3 y = x 4 and passes through the point ( −2 , 1 ) .

y = −3 x 5

Got questions? Get instant answers now!

For the following exercises, find the equation of the line using the given information.

( 2 , 0 ) and ( −2 , 5 )

Got questions? Get instant answers now!

( 1 , 7 ) and ( 3 , 7 )

y = 7

Got questions? Get instant answers now!

The slope is undefined and it passes through the point ( 2 , 3 ) .

Got questions? Get instant answers now!

The slope equals zero and it passes through the point ( 1 , −4 ) .

y = −4

Got questions? Get instant answers now!

The slope is 3 4 and it passes through the point (1,4) .

Got questions? Get instant answers now!

( −1 , 3 ) and ( 4 , −5 )

8 x + 5 y = 7

Got questions? Get instant answers now!

Graphical

For the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither.

y = 2 x + 7 y = 1 2 x 4

Got questions? Get instant answers now!

3 x 2 y = 5 6 y 9 x = 6


Coordinate plane with the x and y axes ranging from negative 10 to 10.  The functions 3 times x minus 2 times y = 5 and 6 times y minus 9 times x = 6 are graphed on the same plot.  The lines do not cross.

Parallel

Got questions? Get instant answers now!

y = 3 x + 1 4 y = 3 x + 2

Got questions? Get instant answers now!

x = 4 y = −3


Coordinate plane with the x and y axes ranging from negative 10 to 10.  The function y = negative 3 and the line x = 4 are graphed on the same plot.  These lines cross at a 90 degree angle.

Perpendicular

Got questions? Get instant answers now!

Numeric

For the following exercises, find the slope of the line that passes through the given points.

( 5 , 4 ) and ( 7 , 9 )

Got questions? Get instant answers now!

( −3 , 2 ) and ( 4 , −7 )

m = 9 7

Got questions? Get instant answers now!

( −5 , 4 ) and ( 2 , 4 )

Got questions? Get instant answers now!

( −1 , −2 ) and ( 3 , 4 )

m = 3 2

Got questions? Get instant answers now!

( 3 , −2 ) and ( 3 , −2 )

Got questions? Get instant answers now!

For the following exercises, find the slope of the lines that pass through each pair of points and determine whether the lines are parallel or perpendicular.

( −1 , 3 )   and   ( 5 , 1 ) ( −2 , 3 )   and   ( 0 , 9 )

m 1 = 1 3 , m 2 = 3 ; Perpendicular .

Got questions? Get instant answers now!

( 2 , 5 )   and   ( 5 , 9 ) ( −1 , −1 )   and   ( 2 , 3 )

Got questions? Get instant answers now!

Technology

For the following exercises, express the equations in slope intercept form (rounding each number to the thousandths place). Enter this into a graphing calculator as Y1, then adjust the ymin and ymax values for your window to include where the y -intercept occurs. State your ymin and ymax values.

0.537 x 2.19 y = 100

y = 0.245 x 45.662. Answers may vary. y min = −50 ,   y max = −40

Got questions? Get instant answers now!

4,500 x 200 y = 9,528

Got questions? Get instant answers now!

200 30 y x = 70

y = 2.333 x + 6.667. Answers may vary. y min = −10 ,   y max = 10

Got questions? Get instant answers now!

Extensions

Starting with the point-slope formula y y 1 = m ( x x 1 ) , solve this expression for x in terms of x 1 , y , y 1 , and m .

Got questions? Get instant answers now!

Starting with the standard form of an equation A x  + B y  = C, solve this expression for y in terms of A , B , C , and x . Then put the expression in slope-intercept form.

y = A B x + C B

Got questions? Get instant answers now!

Use the above derived formula to put the following standard equation in slope intercept form: 7 x 5 y = 25.

Got questions? Get instant answers now!

Given that the following coordinates are the vertices of a rectangle, prove that this truly is a rectangle by showing the slopes of the sides that meet are perpendicular.

( −1 , 1 ) , ( 2 , 0 ) , ( 3 , 3 ) , and ( 0 , 4 )

The slope for  ( −1 , 1 )  to  ( 0 , 4 )  is  3. The slope for  ( −1 , 1 )  to  ( 2 , 0 )  is  1 3 . The slope for  ( 2 , 0 )  to  ( 3 , 3 )  is  3. The slope for  ( 0 , 4 )  to  ( 3 , 3 )  is  1 3 .

Yes they are perpendicular.

Got questions? Get instant answers now!

Find the slopes of the diagonals in the previous exercise. Are they perpendicular?

Got questions? Get instant answers now!

Real-world applications

The slope for a wheelchair ramp for a home has to be 1 12 . If the vertical distance from the ground to the door bottom is 2.5 ft, find the distance the ramp has to extend from the home in order to comply with the needed slope.

30 ft

Got questions? Get instant answers now!

If the profit equation for a small business selling x number of item one and y number of item two is p = 3 x + 4 y , find the y value when p = $ 453  and   x = 75.

Got questions? Get instant answers now!

For the following exercises, use this scenario: The cost of renting a car is $45/wk plus $0.25/mi traveled during that week. An equation to represent the cost would be y = 45 + .25 x , where x is the number of miles traveled.

What is your cost if you travel 50 mi?

$57.50

Got questions? Get instant answers now!

If your cost were $ 63.75 , how many miles were you charged for traveling?

Got questions? Get instant answers now!

Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel?

220 mi

Got questions? Get instant answers now!

Questions & Answers

By the definition, is such that 0!=1.why?
Unikpel Reply
(1+cosA+IsinA)(1+cosB+isinB)/(cos@+isin@)(cos$+isin$)
Ajay Reply
hatdog
Mark
how we can draw three triangles of distinctly different shapes. All the angles will be cutt off each triangle and placed side by side with vertices touching
Shahid Reply
bsc F. y algebra and trigonometry pepper 2
Aditi Reply
given that x= 3/5 find sin 3x
Adamu Reply
4
DB
remove any signs and collect terms of -2(8a-3b-c)
Joeval Reply
-16a+6b+2c
Will
is that a real answer
Joeval
(x2-2x+8)-4(x2-3x+5)
Ayush Reply
sorry
Miranda
x²-2x+9-4x²+12x-20 -3x²+10x+11
Miranda
x²-2x+9-4x²+12x-20 -3x²+10x+11
Miranda
(X2-2X+8)-4(X2-3X+5)=0 ?
master
The anwser is imaginary number if you want to know The anwser of the expression you must arrange The expression and use quadratic formula To find the answer
master
The anwser is imaginary number if you want to know The anwser of the expression you must arrange The expression and use quadratic formula To find the answer
master
Y
master
X2-2X+8-4X2+12X-20=0 (X2-4X2)+(-2X+12X)+(-20+8)= 0 -3X2+10X-12=0 3X2-10X+12=0 Use quadratic formula To find the answer answer (5±Root11i)/3
master
Soo sorry (5±Root11* i)/3
master
x2-2x+8-4x2+12x-20 x2-4x2-2x+12x+8-20 -3x2+10x-12 now you can find the answer using quadratic
Mukhtar
2x²-6x+1=0
Ife
explain and give four example of hyperbolic function
Lukman Reply
What is the correct rational algebraic expression of the given "a fraction whose denominator is 10 more than the numerator y?
Racelle Reply
y/y+10
Mr
Find nth derivative of eax sin (bx + c).
Anurag Reply
Find area common to the parabola y2 = 4ax and x2 = 4ay.
Anurag
y2=4ax= y=4ax/2. y=2ax
akash
A rectangular garden is 25ft wide. if its area is 1125ft, what is the length of the garden
Jhovie Reply
to find the length I divide the area by the wide wich means 1125ft/25ft=45
Miranda
thanks
Jhovie
What do you call a relation where each element in the domain is related to only one value in the range by some rules?
Charmaine Reply
A banana.
Yaona
a function
Daniel
a function
emmanuel
given 4cot thither +3=0and 0°<thither <180° use a sketch to determine the value of the following a)cos thither
Snalo Reply
what are you up to?
Mark Reply
nothing up todat yet
Miranda
hi
jai
hello
jai
Miranda Drice
jai
aap konsi country se ho
jai
which language is that
Miranda
I am living in india
jai
good
Miranda
what is the formula for calculating algebraic
Propessor Reply
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
Miranda
Practice Key Terms 7

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play




Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask