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
Ahat [919]
3 years ago
10

a line has a slope of -2/3 for a pair of points on the line. Find the missing coordinate if the points are (-1,y) and (4,7)

Mathematics
1 answer:
masha68 [24]3 years ago
8 0

Answer:

The missing co-ordinate is: (-1,$ \frac{31}{3} $).

Step-by-step explanation:

Given the slope of a line and a point on it, we determine the equation of the line by slope - one point form.

Slope - one point form: (y - y₁) = m(x - x₁)

Where, (x₁,y₁) is the point passing through the line.

Here the slope is $ \frac{-2}{3} $ and the point (x₁,y₁) = (4,7).

Therefore the equation would be:

y - 7 = $ \frac{-2}{3} $(x - 4)

⇒  3y - 21 = -2x + 8

⇒                       2x + 3y - 29 = 0       is the equation of the line.

Now it is given that (-1,y) also passes through the line, this point should satisfy the equation.

⇒ 2(-1) +3y = 29

⇒ 3y = 31  i.e., y = $ \frac{31}{3} $

Therefore, the missing co-ordinate is:   (-1,$ \frac{31}{3} $).

You might be interested in
Two airplanes leave an airport at the same time, the first headed due north and the second at a bearing of N42^ E . At 2:00PM, t
Leno4ka [110]

Answer:

The two airplanes are about 330miles apart.

Step-by-step explanation:

The diagram interpreting the question has been attached to this response.

As shown in the diagram,

i. the airplanes leave at point C.

ii. at 2.00pm the first and second airplanes are at points A and B respectively, where they are 312miles and 487miles away from the starting point C in directions due north and N42E from the point C.

iii. the points A, B and C form a triangle with sides a, b and c.

To solve for the value of c which is the distance between the two planes at 2.00pm, the cosine rule is used.

c² = a² + b² - 2abcosC            --------------(i)

where;

b  = 312miles

a = 487miles

C = 42°

Substitute these values into equation (i) and solve as follows;

c² = (487)² + (312)² - 2(312)(487)cos(42)

c² = (237169) + (97344) - 303888cos(42)

c² = (237169) + (97344) - 303888(0.7431)

c² = 334513 - 225819.1728

c² = 108693.8272

<em>Take the square root of both sides</em>

√c² = √108693.8272

c = 329.69

c ≅ 330miles

Therefore, the two airplanes are far apart by 330miles

3 0
3 years ago
How do I find the length of the sides of a right triangle?
RSB [31]

Answer:

A^2+B^2=C^2

Step-by-step explanation:

(A)^2+(B)^2+(A)+(B)+2Cos(a)=C^2

7 0
3 years ago
Read 2 more answers
Find the equation of the line I in the following picture. The shapes under the lines are squares
julia-pushkina [17]
If you look carefully at the graph, you may see that the slope of the line is
          3-4           -1
---------------- = ------ = m
         7-4             3

thus, you have the slope of the line and two points on the line.  Suppose we
choose the point (4,4) and subst. the known slope and the coordinates of this point into the point-slope formula for the eqn of a str line:

y-y1 = m (x-x1)

y-4 = (-1/3)(x-4)

This is the desired equation.  You could, if you wished, change this into slope-intercept form.
5 0
2 years ago
What is an rational number between 9.5 and 9.7 and include decimal approximation to the nearest hundredth
poizon [28]
On of the solutions could be 9.65
7 0
3 years ago
Write an inequality that represents eight less than three times a number is more than 22
inysia [295]
Let x represent the number.
"three times a number" is 3x
eight less than "three times a number" is 3x-8
"is more than 22" is "> 22"

Your inequality is
  3x-8 > 22
5 0
3 years ago
Read 2 more answers
Other questions:
  • I need hellp quick tha answer are 1,2,3,4,5 / 1,2,3,4,5
    13·1 answer
  • Which triangle is a 30°-60°-90° triangle?<br>A. B. C. or D.
    5·2 answers
  • What is an equation of the line that is perpendicular to y=-3/4x+6 and passes through the point (3,9)
    7·1 answer
  • I need help with this plz
    11·1 answer
  • What’s the slope of a line that passes through the points (-3,7) and (-3, 4)?
    11·2 answers
  • For f(x) = 4x+1, what is the output for the input 5?
    10·1 answer
  • What is |12.8| equal I am so confused
    12·1 answer
  • FOR 47 POINTS PLEASE HELP
    6·1 answer
  • The scale on a road map indicates that 2 inches = 30 miles. How many inches would represent 120 miles on this road map?
    5·1 answer
  • PLease helpp asap!!!! a line passes through the point (2,6) and has a slope of -9 write the equation of the line in point slope
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!