Mathematics : asked on synite
 03.02.2023

write the equation for the line passes through (6,-2) and (-3,1)
pls help

. 10

Step-by-step answer

24.11.2022, solved by verified expert

Faq

Mathematics
Step-by-step answer
P Answered by PhD

y = \frac{1}{2} x - 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \frac{1}{2} x - 3 ← is in slope- intercept form

with m = \frac{1}{2}

Parallel lines have equal slopes, thus

y = \frac{1}{2} x + c ← is the partial equation

To find c substitute (6, - 2) into the partial equation

- 2 = 3 + c ⇒ c = - 2 - 3 = - 5

y = \frac{1}{2} x - 5 ← equation of line

Mathematics
Step-by-step answer
P Answered by PhD

( x + 3)^2 + ( y - 3)^2 = 106

Step-by-step explanation:

The equation of the circle with a center and a point

( x - a) ^2 + ( y - b) ^2 = r^2

( -3 , 3) - center - (a, b)

a = -3

b = 3

( 6 , -2) - point - ( x, y)

x = 6

y = -2

Step 1: substitute the center into the equation

( x -(-3)^2 + ( y - 3)^2 = r^2

( x + 3)^2 + ( y - 3)^2 = r^2

Step 2: sub the point into the equation

( 6 + 3)^2 + ( -2 - 3)^2 = r^2

9^2 + ( -5)^2 = r^2

81 + 25 = r^2

106 = r^2

Step 3: sub the radius into the equation

( x + 3)^2 + ( y - 3)^2 = 106

The equation of the circle is

( x + 3)^2 + ( y - 3)^2 = 106

Mathematics
Step-by-step answer
P Answered by PhD

y = \frac{1}{2} x - 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \frac{1}{2} x - 3 ← is in slope- intercept form

with m = \frac{1}{2}

Parallel lines have equal slopes, thus

y = \frac{1}{2} x + c ← is the partial equation

To find c substitute (6, - 2) into the partial equation

- 2 = 3 + c ⇒ c = - 2 - 3 = - 5

y = \frac{1}{2} x - 5 ← equation of line

Mathematics
Step-by-step answer
P Answered by PhD

( x + 3)^2 + ( y - 3)^2 = 106

Step-by-step explanation:

The equation of the circle with a center and a point

( x - a) ^2 + ( y - b) ^2 = r^2

( -3 , 3) - center - (a, b)

a = -3

b = 3

( 6 , -2) - point - ( x, y)

x = 6

y = -2

Step 1: substitute the center into the equation

( x -(-3)^2 + ( y - 3)^2 = r^2

( x + 3)^2 + ( y - 3)^2 = r^2

Step 2: sub the point into the equation

( 6 + 3)^2 + ( -2 - 3)^2 = r^2

9^2 + ( -5)^2 = r^2

81 + 25 = r^2

106 = r^2

Step 3: sub the radius into the equation

( x + 3)^2 + ( y - 3)^2 = 106

The equation of the circle is

( x + 3)^2 + ( y - 3)^2 = 106

Mathematics
Step-by-step answer
P Answered by PhD

9514 1404 393

  a) y +2 = (4/3)(x -3)

  b) 4x -3y = 18

Step-by-step explanation:

a) The slope formula gives part of what is needed for point-slope form:

  m = (y2 -y1)/(x2 -x1)

  m = (2 -(-2))/(6 -3) = 4/3

Point-slope form is ...

  y -k = m(x -h) . . . . . . for slope m and point (h, k)

Using the first point, we get ...

  y +2 = 4/3(x -3)

__

b) Multiplying by 3 and eliminating parentheses, we get ...

  3(y +2) = 4(x -3)

  3y +6 = 4x -12

Adding 12 -3y to both sides gives ...

  18 = 4x -3y

Putting this in the usual form, we have ...

  4x -3y = 18

Mathematics
Step-by-step answer
P Answered by Specialist
We have a line passing through 3 points. We can use the first
two points to find the equation of the line.
(6,3), (8,4)

slope m = (4-3)/(8-6) = 1/2

We can use the point slope form y-y1 = m(x-x1) or
the slope intercept form y = mx + b
to find the equation of the line.

Let's take the point (6,3) and use y = mx + b to find b
y = 3, x = 6, m = 1/2

3 = (1/2)(6) + b
3 = 3 + b
0 = b

The equation of our line is y = (1/2)x

We have a line of equation y = (1/2)x going through point (n,-2)

Plugging in we have: -2 = (1/2)n
2(-2) = n
-4 = n

Your answer is n = -4

NOTE: looking at the 3 points as given initially: (6,3), (8,4), (n,-2)
We can see that 3 = (1/2)6 and 4 = (1/2)8 so -2 = (1/2)n makes sense

Hope this helps you :)
Mathematics
Step-by-step answer
P Answered by Specialist
\left[\begin{array}{ccc}6&3&1\\8&4&1\\n&-2&1\end{array}\right]=0
6*4*1+3*n*1+8*(-2)*1-1*4*n-6*(-2)*1-8*3*1=0
24+3n-16-4n+12-24=0
3n-4n+\diagup\!\!\!\!\!24-16+12-\diagup\!\!\!\!\!24=0
3n-4n-16+12=0
-n-4=0
Keep the number on the left incognito and Put the number on the right without incognito by changing the sign.
-n =4 simplify by (-1)
\boxed{n = - 4}

\boxed{n = -4}
Mathematics
Step-by-step answer
P Answered by Master
If a line pass through three points, they are collinear points, and the determinant of a matrix produced by their coordinates equals 0.

Knowing this, we can fin the value of n.

We need a triangular matrix, so we can complete it with 1's.

\left[\begin{array}{ccc}6&3&1\\8&4&1\\n&-2&1\end{array}\right]

24 + 3n - 16 - 4n + 12 - 24 = 0

- n - 4 = 0

- n = 4

n = -4

The value of n it's -4.

Hope it helps.

Try asking the Studen AI a question.

It will provide an instant answer!

FREE