1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mrs_skeptik [129]
3 years ago
14

Write the slope-intercept form of the equation that passes through the given points. (separate equations for each of them)

Mathematics
1 answer:
guajiro [1.7K]3 years ago
6 0

Answer:

Part 1) y=-\frac{1}{5}x-1

Part 2) y=3x-16

Part 3) y=4

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

y=mx+b

where

m is the slope

b is the y-intercept

Part 1) we have

(10,-3) (5,-2)

<u><em>Find the slope</em></u>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute

m=\frac{-2+3}{5-10}

m=\frac{1}{-5}

m=-\frac{1}{5}

<em>Find the value of b</em>

we have

m=-\frac{1}{5}

point (10,-3)

substitute in the equation y=mx+b  and solve for b

-3=-\frac{1}{5}(10)+b

-3=-2+b

b=-3+2=-1

substitute

y=-\frac{1}{5}x-1

Part 2) we have

(6,2) (7,5)

<u><em>Find the slope</em></u>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute

m=\frac{5-2}{7-6}

m=\frac{3}{1}

m=3

<em>Find the value of b</em>

we have

m=3

point (6,2)

substitute in the equation y=mx+b  and solve for b

2=3(6)+b

2=18+b

b=2-18=-16

substitute

y=3x-16

Part 3) we have

(4,4) (-7,4)

<u><em>Find the slope</em></u>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute

m=\frac{4-4}{-7-4}

m=\frac{0}{-11}

m=0

This is a horizontal line (parallel to the x-axis)

The y-intercept b is equal to the y-coordinate

<em>therefore</em>

The equation of the line is

y=4

You might be interested in
Which statements describe a residual plot for a line of best fit that is a good model for a scatterplot? Check all that apply.
Otrada [13]

Answer:

Options 1, 2, & 5 are the correct answers

Just did it

8 0
3 years ago
Robin earned $4,320 in 9 weeks and worked 40 hours in each week. How much did he earn per hour? $ per hour
lys-0071 [83]
Hi.............

Good luck :) ........

8 0
3 years ago
Read 2 more answers
Perimeter, Circumference,
SOVA2 [1]

Answer:

Perimeter = 120 m

Step-by-step explanation:

Perimeter = (24+36)*2 = 120 m

8 0
3 years ago
What is the f(n) runtime of the following pseudocode: sum = 0 for A = N/2 downto 1 for B = 1 to 4N increment sum by B
nikitadnepr [17]

Answer:

f(N) = 2+ N/2 + 6N² units of time.

Step-by-step explanation:

Assigning 0 to the variable sum takes one unit of time.

Each time you increment sum by B, you need to call the value of sum, sum it to B and assign it to sum, which takes three units of time in total. You are repeating this process for each value of B which ranges from 1 to 4n and for each value of A which ranges from 1 to n/2. Opening the FOR takes also another unit of time, so, as a result, we have

f(N) 1 + 1 (open the FOR in A)+ N/2*(1 (open the FOR in B) + 4N*3) = 2+ N/2 + 6N² units of time. It has order complexity O(N²).

5 0
3 years ago
Solve the following differential equation: (1− 5 y +x) dy/dx +y= 5/x −1 .<br><br> C=
Ganezh [65]

Answer:

y(1+x)+x-5\ln xy=C

Step-by-step explanation:

Consider the given differential equation is

(1-\frac{5}{y}+x)\frac{dy}{dx}+y=\frac{5}{x}-1

(1-\frac{5}{y}+x)\frac{dy}{dx}=\frac{5}{x}-1-y

(1-\frac{5}{y}+x)dy=(\frac{5}{x}-1-y)dx

Taking all variables on right sides.

(1-\frac{5}{y}+x)dy-(\frac{5}{x}-1-y)dx=0

(-\frac{5}{x}+1+y)dx+(1-\frac{5}{y}+x)dy=0

Let as assume,

M=-\frac{5}{x}+1+y and N=1-\frac{5}{y}+x

Find partial derivatives \frac{\partial M}{\partial y} and \frac{\partial N}{\partial x}

\frac{\partial M}{\partial y}=1 and \frac{\partial N}{\partial x}=1

Since \frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}, therefore the given differential equation is exact.

The solution of the exact differential equation is

\int Mdx+\int N(\text{without x)}dy=C

\int (-\frac{5}{x}+1+y)dx+\int (1-\frac{5}{y})dy=C

yx-5\ln x+x+y-5\ln y=C

y+x+xy-5\ln x-5\ln y=C

y(1+x)+x-5(\ln x+\ln y)=C

y(1+x)+x-5\ln xy=C

7 0
3 years ago
Other questions:
  • A merchant is selling wind chimes from booth at a flea market he rents his space for $125 per day The Profit from each wind chim
    8·1 answer
  • If the right triangular prism shown has a volume of 15 cubic inches, what is the height of the triangular base of the prism, H?
    8·1 answer
  • Find the slope of the line shown on the graph to the right.
    9·1 answer
  • Kiemanh is solving the equation 15 r minus 6 r = 36. What is the value of r?
    5·2 answers
  • Which of the following represents the characteristics of the graph of x &lt; 4? Please help.
    9·1 answer
  • A takes 3 hours more than B to walk 30 km. But if A doubles his pace, he is ahead of B by 3/2 hours . Find their speed of walkin
    11·1 answer
  • For all values of x, f(x) = 2x-3 and g(x) = x^2 + 1 a) Find fg(x) Simplify and give your answer in the form ax^2 + b b) Find gf(
    13·1 answer
  • 6th grade work !! pls help
    6·1 answer
  • Solve for : 6−11−13&lt;7−5
    7·1 answer
  • Simplify 3 ∙ 2x. What is the coefficient? x 2 6 3
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!