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
Lena [83]
3 years ago
15

Find equation of straight line which

Mathematics
1 answer:
kenny6666 [7]3 years ago
8 0

Answer:

The required equation is: y = -\frac{8}{5}x+\frac{127}{25}

Step-by-step explanation:

The slope-intercept form of a line is given by:

y = mx+b

For writing equation of a line, slope and a point is needed from which the line passes.

In order to find the slope of line perpendicular to PQ, we have to find slope of PQ first.

Slope is denoted by m and given by the formula

m = \frac{y_2-y_1}{x_2-x_1}

Given points are:

P(-1, -4) and Q (7, 1)

Putting the values

m = \frac{1-(-4)}{7-(-1)}\\m = \frac{1+4}{7+1} = \frac{5}{8}

The product of slope of two pependicular lines is -1

Let m1 be the slope of line perpendicular to PQ

m.m_1 = -1\\\frac{5}{8}.m_1 = -1\\m_1 = \frac{8}{5} * -1\\m_1 = -\frac{8}{5}

Now for the point, we have to find the point that divides PQ in ratio 3:2

The formula is:

(x,y) = (\frac{nx_1+mx_2}{m+n} , \frac{ny_1+my_2}{m+n})\\

Here

m = 3

n= 2

Putting the values

(x,y) = (\frac{(2)(-1)+(3)(7)}{3+2} , \frac{(2)(-4)+(3)(1)}{3+2})\\= (\frac{-2+21}{5} , \frac{-8+3}{5})\\=(\frac{19}{5} , \frac{-5}{5})\\=(\frac{19}{5} , -1)

So we have to write equation of a line with slope -8/5 and passing through point (19/5, -1)

Putting the values in slope-intercept form

y = -\frac{8}{5}x +b

Putting the point in the equation

-1 = -\frac{8}{5} (\frac{19}{5}) + b\\-1 = -\frac{152}{25} + b\\b = -1+\frac{152}{25}\\b = \frac{-25+152}{25}\\b = \frac{127}{25}

Putting the value of b

y = -\frac{8}{5}x+\frac{127}{25}

Hence,

The required equation is: y = -\frac{8}{5}x+\frac{127}{25}

You might be interested in
Graph the function f(x)=32x−4. Use the line tool and select two points to graph.
muminat

Answer:

I believe the points (0,-4) and (1,28) work. You can also use (0.125,0) if you can.

4 0
3 years ago
Read 2 more answers
The ordered pairs
Paul [167]

Answer:

Step-by-step explanation:

Slope of the line through (0,3) and (2,5) = (5-3)/(2-0) = 1.

Equation of line: y = x+3

When x=3, y=6

(3,n) = (3,6)

5 0
3 years ago
For what values of k will he graph of y=kx+3 be a descending line
liraira [26]
K has to be negative.
3 0
3 years ago
Read 2 more answers
Find the value of i77.<br> A) 1 <br> B) i <br> C) −1 <br> D) −i
Colt1911 [192]

assuming you mean i^{77} where i=\sqrt{-1}

ok, notice a pattern in the exponent

i^1=i=\sqrt{-1}

i^2=-1

i^3=-\sqrt{-1}=-i

i^4=1

i^5=i=\sqrt{-1}

hum, so it goes 1,2,3,4, then repeats

ok, so every 4, the cycle repeats

how far  up is 77 from a multipule of 4?

4*19=76

76 is 1 away from 77

so i^{77}=(i^{76})(i^1)=

(i^4)^{19}(i)=(1)^{19}i=i

the answer is B

8 0
3 years ago
Read 2 more answers
Which is larger 10.5 or 10.50
Bumek [7]

Answer:

10.5 is really 10.50 the . 5 is half the whole one unit, like 50 cents is half a dollar

7 0
3 years ago
Other questions:
  • Please help!!!! I dont know how to do this and also please explain!
    11·1 answer
  • A speed that is greater than 32 miles per hour
    13·1 answer
  • BRANLIEST TO FIRST CORRECT ANSWER:
    14·1 answer
  • Given that m angle KLH=120^ which statement about the must be true? angle HLM is bisected by angle GLJ is bisected by vec LH . m
    9·1 answer
  • What is the inequality?
    10·1 answer
  • Angela Spangler credit card statement to purchase a new backpack for $28 and bought her sister birthday gift for $45 she made a
    10·1 answer
  • How is 2.47 and 24,700 different
    7·2 answers
  • EQUATIONS AND INEC
    6·1 answer
  • The number of children's movie tickets sold over a period of a week is
    5·1 answer
  • On Wednesday 28% of the customers who bought gas at a gas station made additional purchases. There were 300 customers who bought
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!