Equation of the Line
Lesson
I
After going through this lesson, you are expected to find the equation of a
line given (a) two points, (b) the slope and a point and (c) the slope and its
intercepts
From the given linear equation, we can determine 2 points that will satis-
fy the equation. Also we can determine the slope and the y- intercept so as the
x and y intercepts.
Example: Given - 2x + y = 6
Find: a. two points that will satisfy the equation
(b) slope and y-intercept
(c) x and y intercept
Solution:
(a) -2x + y = 6
If x = -1
If y = 2
-21-1) + y = 6
- 2x + 2 = 6
2 + y = 6- y = 4
-2x = 4-x= -2
The point is (-1,4)
The point is (-2, 2)
(b) Change the equation to slope intercept form : y = 2x + 6
Therefore the slope m = 2 and the y-intercept b = 6
(c) Find the and y intercept of -2x + y = 6
Let x = 0, -2(0) + y = 6; y = 6. the intercept is (0,6)
Let y = 0, -2x + 0 = 6; -2x = 6, X = -3, the y intercept is (-3,0)
Learning Task 1 : From the given equation of the line a) find two points that will
satisfy the equation, b) the slope and the y intercepts and c) the x and y-
intercepts.
2.
3y - X9
1. 3x + 2y = 5
9514 1404 393
Answer:
a) (0, 5/2), (5/3, 0)
b) m = -3/2; b = 5/2
c) (5/3, 0), (0, 5/2)
Step-by-step explanation:
Given:
3x +2y = 5
Find:
a) two points that satisfy the equation
b) slope and y-intercept
c) x-intercept
Solution:
Since the intercepts are points on the line, finding them satisfies all parts of the question except finding the slope.
a) Let x=0. Then we can find y from ...
3·0 +2y = 5
y = 5/2
One point is (0, 5/2).
Let y=0. Then we can find x from ...
3x +2·0 = 5
x = 5/3
Another point is (5/3, 0).
Two points on the line are (0, 5/2) and (5/3, 0).
__
b) The slope can be found using the slope formula on the two points we found.
m = (y2 -y1)/(x2 -x1)
m = (0 -5/2)/(5/3 -0) = -(5/2)/(5/3) = -3/2
The slope is -3/2. The y-intercept is 5/2.
__
c) The x- and y-intercepts are (5/3, 0) and (0, 5/2), respectively.
Which equation represents the graphed function?
10,3)
(32)
2
5
-3 -2 -1
1
3
4 5
-2
DR
Or
A
y = -3x + 3
B
y=-{x+3
С
y = 3x -
D
y = 3x - 3
Answer:
the equation is y=-1/3x+3
Find (x^3+7x^2-16x-112) divide (x+4) by using synthetic division.
Answer:
x^2+3x-28
Step-by-step explanation:
Answer:
The answer is x^2 3x 28
Step-by-step explanation:
help me please I have no idea what the answer is
Answer:
-21/10
Step-by-step explanation:
-2/5 - 4/5 = -6/5 <--
a common denominator
Then...
-6/5 -9/10 = -21/10
There is not a common denominator so you have to multiply 2 to the -6/5 to make it -12/10
The answer can be left as an improper fraction which is -21/10
or a mixed number -2 1/10 th
A recipe for shepherd's pie uses 3 cups potatoes, 2 cups carrots, 1 cup onions, 1 ½ cups ground round to create enough for 6 people. If you need to feel 16 people, how many cups of carrots do you need? Use scale factors and ratios to solve this problem. Remember to show your work.
Answer:
[tex]5\frac{1}{3}[/tex] cups of carrot.
Step-by-step explanation:
Let's set up proportional equation.
6 people need 2 cups of carrots
Let 16 people need x cups of carrots.
We could form ratio for number of people to cups of carrot used as
6:2
16:x
So, proportional equation would be
[tex]\frac{2}{6} =\frac{x}{16}[/tex]
Cross multiply
32=6 x
Divide both sides by 6.
x=[tex]\frac{32}{6}[/tex]
Divide to get mixed number
x=5[tex]\frac{2}{6}[/tex]
Simplify the fraction
x=[tex]5\frac{1}{3}[/tex] cups of carrot.
Which expression is not equivalent to -3x + 24? Select all that apply.
A. -3(x - 8)
B. -(3x + 24)
C. 3/2(-2x + 16)
D. -1/3( 9x + 8)
E. 6(-1/2x - 4)
F. 8(-3/8x + 3)
Answer:
B, D, and E
Step-by-step explanation:
You'll have to distribute each and put them into a full equation again.
A. -3x + 24
B. -3x - 24
C. -3x + 24
D. -3x - 8/3
E. -3x - 24
F. -3x + 24
I bolded the ones that did not equal -3x + 24
so your answer is B, D, and E
URGENTTTTTTTTTTTTTTT ASAP MARKING BRAINLIEST
Answer:
I would say B only IV because all of the others are assuming and there's no way to prove true or not.
Step-by-step explanation:
What is the slope of the line between (-3, 6) and (11,-5)?
Answer:
m=-11/14
Step-by-step explanation:
What is the domain of the square root function graphed below?
x=-1 x>/=-1
Answer:
im guessing -1
Step-by-step explain
well it would be greater than -1x-1
Use the Distributive Property and mental math to find the product.
9×76 =
Answer:
684
Step-by-step explanation:
Trust
Y greater than or less than 1/4 X + 2
Answer:
y[tex]\geq[/tex]1/4x+2
Step-by-step explanation:
HURRY PLEASE!!
How would you graph this on a slope?
Answer:
If you wanted to you could go to desmos it helps you graph
Step-by-step explanation:
transversals angles
the answer of your question is angle 3
emily is entering a bicycle race for charity. her mother pledges $0.40 for every 0.25 mile she bikes. if emily bikes 6 miles how much will her mother donate
Answer:
$9.60
Step-by-step explanation:
0.40(6/0.25)
0.40(24)
9.6
Answer:
the correct answer is $2.40
Step-by-step explanation:
0.40= every 0.25miles
for 6 miles it will be 2.40 because u multiply 6 with 0.40 and u get the answer
Sarah and Henry share some sweets in the ratio 5:6 .
Sarah eats 16 of her sweets and the ratio of sweets left becomes 1:2 .
How many sweets did Henry have?
Jana has a sandbox that is 4 1/2 feet long, 5 feet wide, and 1/2 foot deep. How many cubic feet of sand does she need to fill the sandbox completely.
Answer:
She needs to fill [tex]11\frac{1}{4}[/tex] ft³ in order to fill the sandbox completely.
Step-by-step explanation:
length = [tex]l[/tex]= [tex]4\frac{1}{2}=\frac{9}{2}=4.5[/tex] feet
width = [tex]w=[/tex] 5 feet
depth = [tex]h=\frac{1}{2}=0.5[/tex] feet
Sandbox is just like a rectangular prism. In order to fill the sandbox completely, we need to determine the volume.
Thus, the formula to find the volume of a rectangular prism can be computed using the formula
[tex]V\:=\:l\:\times \:w\:\times \:h[/tex]
[tex]V=4\frac{1}{2}\times 5\times \frac{1}{2}[/tex]
[tex]=\frac{9}{2}\times \:\:5\times \:\frac{1}{2}[/tex]
[tex]=\frac{45}{2\times \:2}[/tex]
[tex]=11\frac{1}{4}[/tex] ft³
Thus, she needs to fill [tex]11\frac{1}{4}[/tex] ft³ in order to fill the sandbox completely.
Need help ASAP!!!!!!!!!!!
Answer:
Step-by-step explanation:
5/6 + 1/8 + 3/4 = 1 17/24
Option A is the correct answer
How do you graph 16x-4y=2?
Answer:
I like your cut g
Step-by-step explanation:
The ratio of 8 less than a number to 28 more than that number is 2 to 5. What is the number?
a. 32
b. 30
c. 28
d. 15
Answer:
let the number be x
then
(x-8): (x+28) = 2:5
on solving
5x-40= 2x+56
3x = 96
x = 32
Step-by-step explanation:
50pts ANSWER ALL QUESTIONS
13.) -3/4
14.) takes a lot of work
15.)5
16.) corresponding
14.) d=24
15.)25x+5=26x
Answer:
13.) -3/4
14.) takes a lot of work
15.)5
16.) corresponding
14.) d=24
15.)25x+5=26xStep-by-step explanation:
WHICH OF THE FOLLOWING IS THE SLOPE?
Translate into an equation: "The difference of half a number and 7 is the same as the sum of the number and 13"
Answer:
n2 - 7 = n + 13
A Sweater That normally costs $25.00 is on sale for 10 percent Off.
What will the Discount be?
what will the cost of the Sweater be?
Can Someone Please PLEASE help me??
Answer:
15.00
Step-by-step explanati
the discount is 15% because you need to subtract it
5) Find the equation of the line going through the point (4,1) and
perpendicular to y = - 3x +7
Answer:
3y=x-1 OR y=⅓x-⅓
Step-by-step explanation:
Lets call the equation y=-3x+7 line l1
the other line passing through (4,1) l2
If two lines are perpendicular,then the product of their roots=-1
That is m(l1)×m(l2)=-1
Slope of l1=-3 therefore slope of l2=-1÷-3=⅓
Now that we have determined the slope of l2 we move on to find it's equation using the point-slope form
y-y1=m(x-x1)
y-1=⅓(x-4)
3y-3=x-4
3y=x-4+3
3y=x-1 OR y=⅓x-⅓
Solve for x !!!!!!!!!!!!!!!!
Answer:
-9
Step-by-step explanation:
180=85+44+60+(x)-9
Answer:
A. -9
Step-by-step explanation:
A triangle equals 180 degrees so:
60 + 85 + x + 44 = 180
add like terms
x + 189 = 180
subtract 189 from both sides
x = -9
3 values greater than |-3.5|
Answer:
6.5
Step-by-step explanation:
3.5 + 3
Answer:
6.5
Step-by-step explanation:
I-3.5I = 3.5
3.5 + 3 = 6.5
Check Work:
6.5 - 3.5 = 3
or
I-3 - 3.5I = I-6.5I = 6.5
What is mZG?
Enter your answer in the box.
FGH
(x-5)°
(3x+24)°
x°
Answer:
The angle for G is 121°.
Step-by-step explanation:
Given that total angles in a triangle is 180° so in order to find the angle of G, first, you hav eto find the value of x :
x + (x - 5) + (3x + 25) = 180°
5x + 20° = 180°
5x = 160°
x = 32°
Next, you have to find the angle of G :
G = 3x + 25
G = 3(32) + 25
G = 96° + 25°
G = 121°
If and θ is in quadrant IV, and .
Answer:
No hablo espanol
Step-by-step explanation:
Seriously what are you saying XD
You have enough inventory ($3,000,000) to last 30 days for the current orders being processed. However, a new order came in today, which has to be fulfilled in 15 days. This new order will deplete your inventory completely by that time. How much money in inventory must be ordered to last the month?
Answer:
Picture Below
Step-by-step explanation:
HELP ME PLEASE!!Dominic invested $19,000 in an account paying an interest rate of 6.1% compounded monthly. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 16 years?
Answer:
A≈50298
Step-by-step explanation:
The money to the nearest dollar would be in the account after 16 years is to be considered as the $50,298.
Calculation of the future amount:Since
The interest rate be like = 6.1% = 6.1% / 12 = 0.51%
The time period = 16 * 12 = 192
The present value = $1,9000
The PMT is = $0
Now the following formula is used;
So,
= -FV(RATE,NPER,PMT,PV,TYPE)
After applying it, the future value should be $50,298.
Learn more about rate here: brainly.com/question/24546293