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
Mashutka [201]
3 years ago
11

"Write two equations: one parallel, one perpendicular to (5,-2) y= 1/5x-3

Mathematics
2 answers:
guajiro [1.7K]3 years ago
7 0

Answer:

For parallel:

gradient is 1/5

y = mx + c

consider (5, -2):

- 2 = ( \frac{1}{5}  \times 5) + c \\  - 2 = 1 + c \\ c =  - 3

{ \boxed{ \bf{equation : y =  \frac{1}{5}x - 3 }}}

For perpendicular:

gradient, m1:

m _{1} \times m_{2} =  - 1 \\ m _{1} \times  \frac{1}{5}  =  - 1 \\  \\ m _{1} =  - 5

gradient = -5

y = mx + c \\  - 2 = (5 \times -  5) + c \\  - 2 =  - 25 + c \\ c =  23

{ \boxed{ \bf{equation :y =  - 5x + 23 }}}

iren [92.7K]3 years ago
5 0

Answer:

Parallel: y=\displaystyle \frac{1}{5}x-3

Perpendicular: y=-5x+23

Step-by-step explanation:

Hi there!

<u>What we must know:</u>

  • Slope intercept form: y=mx+b where <em>m</em> is the slope and <em>b</em> is the y-intercept (the value of y when the line crosses the y-axis)
  • Parallel lines always have the same slope
  • Perpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2, -6/7 and 7/6)

<u>Finding the Parallel Line</u>

y=\displaystyle \frac{1}{5} x-3

Given this equation, we can identify that its slope (<em>m</em>) is \displaystyle \frac{1}{5}. Because parallel lines always have the same slope, the slope of the line we're currently solving for would be \displaystyle \frac{1}{5} as well. Plug this into y=mx+b:

y=\displaystyle \frac{1}{5}x+b

Now, to find the y-intercept, plug in the given point (5,-2) and solve for <em>b</em>:

-2=\displaystyle \frac{1}{5}(5)+b\\\\-2=1+b\\-2-1=b\\-3=b

Therefore, the y-intercept is -3. Plug this back into y=\displaystyle \frac{1}{5}x+b:

y=\displaystyle \frac{1}{5}x+(-3)\\\\y=\displaystyle \frac{1}{5}x-3

Our final equation is y=\displaystyle \frac{1}{5}x-3.

<u>Finding the Perpendicular Line</u>

y=\displaystyle \frac{1}{5} x-3

Again, the slope of this line is \displaystyle \frac{1}{5}. The slopes of perpendicular lines are negative reciprocals, so the slope of the line we're solving for would be -5. Plug this into y=mx+b:

y=-5x+b

To find the y-intercept, plug in the point (5,-2) and solve for <em>b</em>:

-2=-5(5)+b\\-2=-25+b\\-2+25=b\\23=b

Therefore, the y-intercept is 23. Plug this back into y=-5x+b:

y=-5x+23

Our final equation is y=-5x+23.

I hope this helps!

You might be interested in
What is the simplified of this?
masha68 [24]
It is the second option, let me know if you got it right
6 0
3 years ago
What is the equation of the following line written in slope intercept form (1,5) (-1,-5)
wlad13 [49]
-5-5/-1-1=
-10/-2=
5

y-5=5(x-1)
y-5=5x-5
y=5x+0
6 0
3 years ago
Evaluate the following when x = 3<br> 2x+ 5(x)
Nina [5.8K]

Hi!

I can help you with joy!

Evaluate:

\fbox{2x+5x} when \fbox{x=3}

First, add x's:

\rm{7x}

Now, plug in the value of x (3)

\rm{7(3)

Multiply:`

\rm{21} (Answer)

Hope it helps!

Ask me if you have any doubts.

  • Enjoy Your Day/Night! :)

<em>Answered by</em>

<em>~</em>Silent~

4 0
2 years ago
How many solutions does 9x - 18 = 3(3x - 6) have?
lys-0071 [83]

Answer:

assuming the three options are no solutions, one solution and all real numbers, i would say the final option. i forgot what the proper wording is thoough

7 0
3 years ago
Read 2 more answers
A 45-year-old client diagnosed with colon cancer states, "I do not want any treatment. I have not seen any family members in 25
Kruka [31]

Answer:

3,2,1,4

Step-by-step explanation:

I am a loner, I have not seen any of my family in 25 years, beside, i will decide when and how i want to die. I do not want any treatment.

7 0
3 years ago
Read 2 more answers
Other questions:
  • What is the percent of change if 90 is decreased to 82
    10·2 answers
  • If the radius of a cylinder is 3 centimeters, then will the area of one of the circular bases is 18.84 square centimeters
    15·2 answers
  • Select all that apply. Which of the following represent the same ratio?
    5·2 answers
  • Which point lies on the graph of f(x) = -2(x + 3) – 5 A) (-6,1) B) (-6,-8) C) (6,-13) D) (6,-4)
    5·1 answer
  • 25 - [2x(18 divided by 3) + 2
    7·1 answer
  • Select all the correct locations on the table.
    7·2 answers
  • (9x - 2)<br> (5x + 54)<br> (10y + 6)<br><br> what is the value of x and y
    9·2 answers
  • What is the approximate volume of a cone with a height of 6 mm and radius of 18
    14·2 answers
  • 3x – 15 = 39<br> =<br> What does x equal
    10·2 answers
  • Astronomers often measure large distances using astronomical units (AU) where 1 AU is the average distance from Earth to the Sun
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!