Writing Equations of Lines Given the Graph
Write the slope-intercept form of the equation of each line.
questions are on the image below :)
Answers
Answer:
1. [tex]y = 3x[/tex]
2. [tex]y = -\frac{2}{3}x + 1[/tex]
3. [tex]y = -\frac{2}{3}x - 4[/tex]
4. [tex]y = 4[/tex]
5. [tex]y = x + 5[/tex]
6. [tex]y= \frac{5}{2}x[/tex]
7. [tex]y = -7x -16[/tex]
8. [tex]y = x + 4[/tex]
Step-by-step explanation:
The steps to solving these questions involve
1. Calculate slope using: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
2. Calculate the line equation using point slope formula: [tex]y - y_1 = m(x - x_1)[/tex]
We'll apply the steps above in solving 1 through 8
Solving (1):
When x = 0; y = 0
When x = 1; y = 3
i.e.
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (1,3)[/tex]
Calculate slope:
[tex]m=\frac{3 - 0}{1 - 0}[/tex]
[tex]m=\frac{3 }{1 }[/tex]
[tex]m = 3[/tex]
Next, we calculate the equation
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
[tex](x_1,y_1) = (0,0)[/tex] and [tex]m = 3[/tex]
[tex]y - 0 = 3(x - 0)[/tex]
[tex]y = 3x[/tex]
Solving (2):
When x = 0; y = 1
When x = 3; y = -1
i.e.
[tex](x_1,y_1) = (0,1)[/tex]
[tex](x_2,y_2) = (3,-1)[/tex]
Calculate slope:
[tex]m=\frac{-1 - 1}{3 - 0}[/tex]
[tex]m= -\frac{2}{3}[/tex]
Next, we calculate the equation
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
[tex](x_1,y_1) = (0,1)[/tex] and [tex]m= -\frac{2}{3}[/tex]
[tex]y - 1 = -\frac{2}{3}(x - 0)[/tex]
[tex]y - 1 = -\frac{2}{3}(x)[/tex]
[tex]y - 1 = -\frac{2}{3}x[/tex]
[tex]y = -\frac{2}{3}x + 1[/tex]
Solving (3):
When x = 0; y = -4
When x = -3; y = -2
i.e.
[tex](x_1,y_1) = (0,-4)[/tex]
[tex](x_2,y_2) = (-3,-2)[/tex]
Calculate slope:
[tex]m=\frac{-2 - (-4)}{-3 - 0}[/tex]
[tex]m=\frac{-2 +4}{-3 - 0}[/tex]
[tex]m=\frac{2}{-3}[/tex]
[tex]m=-\frac{2}{3}[/tex]
Next, we calculate the equation
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
[tex](x_1,y_1) = (0,-4)[/tex] and [tex]m= -\frac{2}{3}[/tex]
[tex]y - (-4) = -\frac{2}{3}(x - 0)[/tex]
[tex]y +4 = -\frac{2}{3}(x)[/tex]
[tex]y +4 = -\frac{2}{3}x[/tex]
[tex]y = -\frac{2}{3}x - 4[/tex]
Solving (4):
When x = 0; y = 4
When x = 4; y = 4
i.e.
[tex](x_1,y_1) = (0,4)[/tex]
[tex](x_2,y_2) = (4,4)[/tex]
Calculate slope:
[tex]m=\frac{4 - 4}{4 - 0}[/tex]
[tex]m=\frac{0}{4}[/tex]
[tex]m = 0[/tex]
Next, we calculate the equation
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
[tex](x_1,y_1) = (0,4)[/tex] and [tex]m = 0[/tex]
[tex]y - 4 = 0(x - 0)[/tex]
[tex]y - 4 = 0[/tex]
[tex]y = 4[/tex]
Solving (5):
When x = -4; y = 1
When x = -1; y = 4
i.e.
[tex](x_1,y_1) = (-4,1)[/tex]
[tex](x_2,y_2) = (-1,4)[/tex]
Calculate slope:
[tex]m=\frac{4 - 1}{-1 - (-4)}[/tex]
[tex]m=\frac{4 - 1}{-1 +4)}[/tex]
[tex]m=\frac{3}{3)}[/tex]
[tex]m = 1[/tex]
Next, we calculate the equation
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
[tex](x_1,y_1) = (-4,1)[/tex] and [tex]m = 1[/tex]
[tex]y - 1 = 1(x - (-4))[/tex]
[tex]y - 1 = 1(x +4)[/tex]
[tex]y - 1 = x +4[/tex]
[tex]y = x +4 + 1[/tex]
[tex]y = x + 5[/tex]
Solving (6):
When x = 0; y = 0
When x = 2; y = 5
i.e.
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (2,5)[/tex]
Calculate slope:
[tex]m=\frac{5 - 0}{2 - 0}[/tex]
[tex]m=\frac{5 }{2 }[/tex]
Next, we calculate the equation
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
[tex](x_1,y_1) = (0,0)[/tex] and [tex]m=\frac{5 }{2 }[/tex]
[tex]y - 0 = \frac{5}{2}(x - 0)[/tex]
[tex]y - 0 = \frac{5}{2}(x)[/tex]
[tex]y= \frac{5}{2}x[/tex]
Solving (7):
When x = -2; y = -2
When x = 2; y = 5
i.e.
[tex](x_1,y_1) = (-2,-2)[/tex]
[tex](x_2,y_2) = (-3,-5)[/tex]
Calculate slope:
[tex]m=\frac{5 - (-2)}{-3 - (-2)}[/tex]
[tex]m=\frac{5 +2}{-3 +2}[/tex]
[tex]m=\frac{7}{-1}[/tex]
[tex]m =-7[/tex]
Next, we calculate the equation
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
[tex](x_1,y_1) = (-2,-2)[/tex] and [tex]m =-7[/tex]
[tex]y - (-2) = -7(x - (-2))[/tex]
[tex]y +2 = -7(x +2)[/tex]
[tex]y +2 = -7x -14[/tex]
[tex]y = -7x -14 - 2[/tex]
[tex]y = -7x -16[/tex]
Solving (8):
When x = -3; y = 1
When x = 0; y = 4
i.e.
[tex](x_1,y_1) = (-3,1)[/tex]
[tex](x_2,y_2) = (0,4)[/tex]
Calculate slope:
[tex]m = \frac{4 - 1}{0 - (-3)}[/tex]
[tex]m = \frac{4 - 1}{0 +3}[/tex]
[tex]m = \frac{3}{3}[/tex]
[tex]m = 1[/tex]
Next, we calculate the equation
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
[tex](x_1,y_1) = (-3,1)[/tex] and [tex]m = 1[/tex]
[tex]y - 1 = 1(x - (-3))[/tex]
[tex]y - 1 = 1(x +3)[/tex]
[tex]y - 1 = x +3[/tex]
[tex]y = x + 3 + 1[/tex]
[tex]y = x + 4[/tex]
Related Questions
I honestly have no idea how to do this and I’m confused .
Answers
Answer:
domain -5,4,11
range-3,0,3
Step-by-step explanation:
Is 0.2525 repeating decimal
Answers
Answer:
If it continues, yes, but if it just stops at 0.2525, no.
Step-by-step explanation:
Compound Inequalities
Solve for x.
−9x+5<17 AND 13x+25<−1
Answers
Answer:
[tex]x>-\frac{4}{3}[/tex] AND [tex]x<-2[/tex]
Step-by-step explanation:
-9x + 5 < 17 AND 13x + 25 < -1
13x + 25 < -1
Subtract 25 from both sides;
13x < -26
Divide both sides by 13;
x < -2
-9x + 5 < 17
Subtract 5 from both sides;
-9x < 12
Divide both sides by -9
x > [tex]-\frac{12}{9}=-\frac{4}{3}[/tex]
f(x)=20x when x is 0.25
Answers
Answer:
5
Step-by-step explanation:
just take the x away from the 20 and multiply 20(0.25)
Pretty easy when u know what you're doing
4. Find the slope and y-intercept of the line 5x – 8y = -20.
Answers
Answer:
Slope is 5/8.
y-intercept is (0, 5/2)
Step-by-step explanation:
Answer:
this is what u need to do
Step-by-step explanation:
first you need to put it into this
[tex]y=mx+b[/tex]
so this is what is next
[tex]y=-8(5x)-20[/tex]
[tex]y=5x+12[/tex]
If Benito is selecting samples of five values from the table, which row will result in the greatest mean? Population Data Row 1 4 2 2 3 3 Row 2 3 3 4 3 2 Row 3 2 4 3 4 3 Row 4 3 4 4 7 3 Row 1 Row 2 Row 3 Row 4
Answers
Explanation
Row 1 - 4+2+2+3+3 = 14 / 5 = 2.8
Row 2 - 3+3+4+3+2 = 15 / 5 = 3
Row 3 - 2+4+3+4+3 = 16 / 5 = 3.2
Row 4 - 3+4+4+7+3 = 21 / 5 = 4.2
Answer:
Its row 4 I hope this helps luv <3
Su fila 4 Espero que esto ayuda a luv <3
10 points plus brainliest! Plz help!
Answers
1/4 x 16= 4
4x3 =12
———————————
Hope this helps :)
The Panthers got possession of
the football on their own 35 yard
line. They ran for an 8 yard gain.
The next play was a 13 yard
loss. What is their field position
after the two plays
Answers
Answer:
56
Step-by-step explanation:
? Question
A bike shop offers three kinds of cycles-tricycles, bicycles, and unicycles. Together, the cycles in the shop have a total of
98 wheels and 46 seats. (Tricycles have 3 wheels, bicycles have 2 wheels, and unicycles have 1 wheel. All cycles have 1 seat.)
There are twice as many bicycles as tricycles. How many of each type of cycle are in the shop?
Answers
Answer:
Number of Uni Cycles = 7
Number of Bi Cycles = 26
Number of Uni Cycles = 39
Total Wheels = 98
Total Seats = 46
Step-by-step explanation:
Uni Cycles consist of 1 wheel
7 x 1 = 7 wheels
Bi Cycles consist of 2 wheels (twice than tri cycle)
26 x 2 = 52 wheels
Tri Cycles consist of 3 wheels
13 x 3 = 39 wheels
Total seats = 7 + 26 + 13 = 46
Total wheels = 7 + 52 + 39 = 98
The number of cycles is given below:-
Number of Uni Cycles = 7
Number of Bi Cycles = 26
Number of Uni Cycles = 39
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Total Wheels = 98
Total Seats = 46
Uni Cycles consist of 1 wheel
7 x 1 = 7 wheels
Bi Cycles consist of 2 wheels (twice as tricycle)
26 x 2 = 52 wheels
Tri Cycles consist of 3 wheels
13 x 3 = 39 wheels
Total seats = 7 + 26 + 13 = 46
Total wheels = 7 + 52 + 39 = 98
To know more about an expression follow
https://brainly.com/question/28794871
#SPJ2
I forgot how to do this, can someone help
Answers
Answer:
B, no need to use calculator, a negative number minus a positive number is a negative number
Step-by-step explanation:
Please help I’ll mark you as brainiest
Answers
Answer:
V = 10 x 9 x (1/3)
V = 30 in³
Step-by-step explanation:
Drop answers...........
Answers
Answer:
A
Step-by-step explanation:
Hope this helps
The recipe for 1 batch of cookies calls for ¾ cups of sugar. How many cups of sugar do you need for ½ a batch of cookies?
Answers
Answer:
3/8 cups of sugar.
Step-by-step explanation:
By multiplying the denomintor by 2 you can get half of what it was.
which integer is greater.
l-5l or l3l
Answers
Answer:
l-5l
Step-by-step explanation:
when a number is in those bars, it means you need to find absolute value, which is how far away a number is from 0. so the two numbers are equal to 5 and 3, and 5 is greater, so choose the first one. to find absolute value, just get rid of the signs, and thats your answer. :)
Pls mark brainliest owo
Answer:
l-5l
Explanation:
l-5l = 5
hannah's allotment is a rectangle and has an area of 188m². if the length of the allotment is 12m, what is its perimeter? give your answer in metres (m).
Answers
Answer:
P = 55.33 meters
Step-by-step explanation:
A=188(m^2)= L*W
L=12m
A/L=W
(188/12) meters=W=47/3
P=2W+2L
P=2(12m) + 2(47/3 m)
= 24 + 94/3 meters
P = 55.33 meters
What is the unit rate $1.79 for 15 oz rounded to nearest tenth
Answers
Answer:
$0.119... per oz, or 0.1
Step-by-step explanation:
$.179 ÷ 15 = 0.119...
Now round to the nearest tenth, and you get 0.1.
What is the value of -3/2 (24-5 1/3)?
Answers
Answer:
-28
Step-by-step explanation:
hope this helps :)
during the flu epidemic 140 students out of the 700 that attended Lincoln academy where absencent what is the percentage of the remaining
Answers
PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSS HELP ME
Ash cannot decide which of two washing machines to buy. The selling price of each is $360. The first is marked down by 30%. The second is marked down by 10% with an additional 20% off. Find the sale price of each washing machine. Use pencil and paper. Explain why ash should buy the first washing machine rather than the second if the machines are the same except for the selling price.
Answers
Answer:
The answer is the first one.
Step-by-step explanation:
Okay, so the first one is solved like this:
You do 360*30%. 30% is 0.3 in decimal form. So 360*0.3=108. 108 is the amount that is discounted, NOT the price. You have to do 360-108, which is 252. The discounted price is $252.
Now the second one is solved like this:
You do 360*10% FIRST because the problem says it was marked 10% BEFORE the 20%. 10%=0.1, so 360*0.1=36. You subtract 360-36, which is 324. Then, you multiply 324 by 20% or 0.2, to get 64.8, which is the discount of 20%. You subtract 324-64.8, which is $259.20. So the first one is the answer because it is cheaper since 252 is less than 259.20. If you need this explanation, don't use this word for word. Summarize this in YOUR own words!
He should by the first washing machine because it cost less than the second washing machine.
Rational Numbers are numbers that
O Can be written as a fraction
O Can not be written as a fraction
O you can think of
O you can imagine
Answers
Answer:
A rational number is a number that can be written as a ratio. That means it can be written as a fraction.
Find the rate of change
1foot 2inches (14inches) 8inches
1foot 2inches (14inches) 8inches
1foot 1inch (13inches) 7.5inches
1foot 5inches (17inches) 8inches
1foot 6inches (18inches) 8inches
Answers
The rate of change is D. 1foot 5inches (17inches) 8inches.
What is the foot?The foot is a measure of a unit of length (or distance) in US units, which equals 12 inches.
The rate of change is the difference between x and y variables. It can be mathematically expressed as Change in input/Change in output. The formula for the rate of change is as follows:
= Δx/Δy
where Δ = change
Calculations:14inches + 8inches = 22inches
13inches + 7.5inches = 20.5inches
18inches + 8inches = 26inches
But 17inches + 8inches = 25inches
Question Completion:Find the rate of change from 2feet 1 inch (25inches) to 8inches.
Thus, the rate of change is D. 1foot 5inches (17inches) 8inches.
Learn more about US units of measurement at https://brainly.com/question/8478667
Answer:
Step-by-step explanation:
d
Can u please help me!
Answers
Answer:
1st one is 20 2nd one is 21
Step-by-step explanation:
Answer:
1: 20
2: 21
im not to sure tho
The sum of four and twice a number is 52
Answers
Answer:
X=24
Step-by-step explanation:
Let a no =X
So
2x+4=52
2x=52-4
2x=48
X=48/2
X=24
So number =24
Fill in the table so it represents a linear function.
Answers
Answer:
(From left to right) 2 5 8
Step-by-step explanation:
1. Find the gap (between the first and last terms) 11 - (-1) = 12
2. Divide by the number of times the linear term is added: 12/4=3
3. Use the common difference to find the missing values.
2. Patients arrive at a hospital accident and emergency department at random follow a
Poisson distribution at a rate of 6 per hour.
(a) Find the probability that, during any 90-minute period, the number of patients
arriving at the hospital accident and emergency department is
(i) exactly 7
(ii) at least 3
(b) What is the mean and standard deviation of the number of patients arriving at the
hospital accident and emergency department in an hour?
Answers
Answer:
a )i) 0.117
ii)0.4126
b)0.7769
Pls help It’s due today:)))))
Answers
Answer:
1.5 i think
Step-by-step explanation:
Answer:
they are all negitive
Step-by-step explanation:
Select the correct answer.
What is the inverse of function f?
f(x) = 7x-3
A. f-1 (x) = 7+x/3
B. f-1(x) =3-7x
C. f-1(x) = 7x+3
D. f-1 (x) = 3- x/7
Answers
Answer:
A
Step-by-step explanation:
Just took the test :)
Can anyone solve this?
Answers
Answer:
Step-by-step explanation:
alternate interior angles
If A = {x | x is an odd integer), B = {x | x is an even integer), C = {2,3,4,5), and D = {3,4,5,6), list the element(s) of the following set.
Answers
Answer:
Answer: 3,4,5,6 can be the complete list for the f(x).
Step-by-step explanation:
Given a polynomial function f(x) which is a fourth degree polynomial .Therefore it must has 4 roots.
Let's check all the options for the possible list of roots of f(x)
1) 3,4,5,6 can be the complete list for the f(x) .
Option 2) and option 3) cannot be the complete list for the f(x) as it has one complex root and complex roots occur in pair.
Option 4) cannot be the complete list for f(x) as complex roots occur in pair and they conjugates but conjugate of 5+i is 5-i(which is not given) not -5+i
Can anyone help me with this? Teacher wants me to do this. No clue where to begin.
16x4+20x(18/2)-10x10=
Answers
Answer:
pemdas?
Step-by-step explanation:
its parentheses then something then you do the multiplication and then divide then add then subtract
