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13.
A line passes through (3, –2) and (6, 2). Write an equation for the line in point-slope form.
Rewrite the equation in standard form using integers.

A. y + 2 = 4/3(x – 3); –4x + 3y = –18
B. y – 3 = 4/3(x + 2); –4x + 3y = 17
C. y + 2 = 4/3(x + 3); –4x + 3y = –18
D. y – 2 = 4/3(x – 3); –4x + 3y = 18

Sagot :

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Answer:

A. y + 2 = 4/3(x – 3); –4x + 3y = –18

Step-by-step explanation:

(3, –2) and (6, 2)

First, we must establish slope...

m=(y-y1)/(x-x1)

m=(-2-2)/(3-6)

m=-4/-3

m=4/3

Point slope formula is...

y-y1=m(x-x1)

Let's select either coordinate.  I randomly select the first (3, –2)...

y--2=4/3(x-3)

Subtracting a negative number is the same as adding a positive number...

y+2=4/3(x-3)

This corresponds to the first answer.

Standard form...

Ax+By=C

y+2=(4/3)x-4

y=(4/3)x-6

-(4/3)x+y=-6

Multiply both sides by 3...

-4x+3y=-18

This also corresponds to the first answer.

 

How about the second coordinate, (6, 2)...

y-y1=m(x-x1)

y-2=(4/3)(x-6)

Let's convert it into standard form..

y-2=(4/3)x-8

y=(4/3)x-6

-(4/3)x+y=-6

Multiply both sides by 3...

-4x+3y=-18

FIRST ANSWER

y + 2 = 4/3(x – 3); –4x + 3y = –18

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