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olga nikolaevna [1]
3 years ago
8

What is the equation of the line that passes through (5, -2) and (-3, 4)?

Mathematics
2 answers:
SpyIntel [72]3 years ago
8 0

Answer:

y = (-3/4)x + 7/4

Step-by-step explanation:

<em>Step 1: Define general form of equation of line</em>

An equation of a straight line on two-dimensional plane could be represented in form of: y = Mx + b, with M is slope and b is y-intercept

<em>Step 2: Set up the system to solve for parameters of equation of line </em>

<em>(solve for M and b)</em>

That equation passes 2 points, which are represented in form of (x, y), (5, -2) and (-3, 4).

Substitute these values of x and y into the original equation in step 1:

-2 = 5M + b

4 = -3M + b

<em>Step 3: Solve the system of equations in step 2 for M and b</em>

Subtract 1st equation from 2nd equation:

     6 = -8M

=> M = -6/8 = -3/4

Substitute M back into 1st equation:

=> -2 = 5*(-3/4) + b

=>  b = -2 + 15/4

=>  b = 7/4

=>  The equation of the line that passes through (5, -2) and (-3, 4):

      y = (-3/4)x + 7/4

Hope this helps!

:)

Sergio [31]3 years ago
3 0

Answer:

Y= -4/3(x-7/2)

Step-by-step explanation:

So first calculate the difference between them,

changes by 8 x units, and -6 y units.

Then substitute them into y/x to find gradient

-6/8 = -4/3

so now we have a part of the equation:

Y= -4/3(x-a)

substitute Y= -2 and x=5 (from (5,-2))

-2= -4/3(5-a)

-2= -20/3+4a/3

Multiply by 3 on both sides

-6= -20+4a

add 20 on both sides

14=4a

a=7/2

use this as the value of a

Y= -4/3(x-7/2)

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