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
WITCHER [35]
3 years ago
12

Find the equation of the line that is parallel to the given line and passes through the given point

Mathematics
1 answer:
Sati [7]3 years ago
5 0

Answer:

\huge\boxed{y=-\dfrac{1}{4}x-1\to x+4y=-4}

Step-by-step explanation:

\text{Let}\ k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\l\ ||\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\==========================\\\\\text{We have}\ x+4y=-6.\\\text{Convert to the slope-intercept form:}\\\\x+4y=-6\qquad\text{subtract}\ x\ \text{from both sides}\\\\4y=-x-6\qquad\text{divide both sides by 4}\\\\y=\dfrac{-x}{4}-\dfrac{6}{4}\\\\y=-\dfrac{1}{4}x-\dfrac{3}{2}\to m_1=-\dfrac{1}{4}

\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (9,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}\\\\x=9,\ y=-3\\\\-3=-\dfrac{1}{4}(9)+b\\\\-3=-\dfrac{9}{4}+b\qquad\text{add}\ \dfrac{9}{4}\ \text{to both sides}\\\\-\dfrac{12}{4}+\dfrac{9}{4}=b\to b=-\dfrac{3}{4}

\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (8,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}

x=8,\ y=-3\\\\-3=-\dfrac{1}{4}(8)+b\\\\-3=-2+b\qquad\text{add 2 to both sides}\\\\-1=b\to b=-1

\text{Therefore the equation is:}\ y=-\dfrac{1}{4}x-1.\\\\\text{Convert to the standard form}\ Ax+By=C:\\\\y=-\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4y=-x-4\qquad\text{add}\ x\ \text{to both sides}\\\\x+4y=-4

You might be interested in
3. Write the numbers given below in scientific notation.<br>(a) 3000000000 ms<br><br>​
k0ka [10]

Step-by-step explanation:

3×10^10 is the scientific notation of 30000000000

8 0
3 years ago
1. Write a numerical expression for the phrase “twelve groups of the sum of fourteen and 10.”
Rom4ik [11]
The expression for five groups of a number added to seventeen.

Let the number be X
Five groups of the number will be 5X
The required expression will be
5(X) +17
6 0
3 years ago
A carnival ride holds 30 people at a time. In one hour,
Olegator [25]

Answer:

7

Step-by-step explanation:

8 0
3 years ago
Hurry <br> due today <br> please <br> thanks
drek231 [11]

Answer:

392.7

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Work out 11. 28- 2.843​
umka21 [38]

Answer:

25.157

Step-by-step explanation:

28-2.843=25.157

4 0
3 years ago
Other questions:
  • What is the most efficient first step to isolate the variable term on one side of this equation?
    9·1 answer
  • Millie needs the average height of the plants she is buying to be atleast 73 inches. She has selected three plants that are 70,
    6·1 answer
  • You typically buy all of your groceries at Grocery Mart. This week, your favorite cereal is on sale there, 4 boxes for $10. At F
    11·1 answer
  • The dance committee has a budget of $125 to decorate the gym for the spring dance. They have already spent $65. Some members wan
    14·2 answers
  • Use the image below, answer the following questions. Be sure to answer all 3 questions in order.
    11·1 answer
  • Rewrite each expression without parentheses:
    14·2 answers
  • 9.812 rounded to the nearest hundredth
    11·1 answer
  • Change 10 m/s in km/h
    10·2 answers
  • PLZZZ HELPPPP ILL MARK BRAINLIEST TO FIRST AND CORRECT ANSWER THAT HAS WORK AND A THX TO SECOND AND CORRECT ANSWER.
    15·1 answer
  • If x2 mx m is a perfect-square trinomial, which equation must be true?.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!