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A line is drawn through (-7,11) and (8,-9). The equation y - 11 = -4/3(x+7) is written to represent a line. Which equations also represent the line?

y = x +
3y = –4x + 40
4x + y = 21
4x + 3y = 5
–4x + 3y = 17

2 Answers

5 votes

Answer:

4x + 3y = 5

Explanation:

Given

y - 11 = -
(4)/(3)(x + 7)

Multiply through by 3

3y - 33 = - 4(x + 7) ← distribute

3y - 33 = - 4x - 28 ( add 4x to both sides )

4x + 3y - 33 = - 28 ( add 33 to both sides )

4x + 3y = 5

User Valentin Harrang
by
7.8k points
6 votes

Answer:

4x+3y=5

Explanation:

We have the equation
y-11=-(4)/(3) (x+7) and the line pass through the points (-7,11) and (8,-9).

We have to find which of the expressions also represents the line. There are two points and there's a way to find the equation that represents the line with those points.

The equation is:


(y-y_(1))/(x-x_(1)) =(y_(2)-y_(1))/(x_(2)-x_(1)),

and the points are
(x_(1),y_(1)) , (x_(2),y_(2))

In this case:


(x_(1),y_(1))=(-7,11)\\(x_(2),y_(2))=(8,-9)

Replacing the points in the equation:


(y-y_(1))/(x-x_(1)) =(y_(2)-y_(1))/(x_(2)-x_(1))\\\\(y-11)/(x-(-7))=((-9)-11)/(8-(-7))\\

Now we have to resolve the equation:


(y-11)/(x-(-7))=((-9)-11)/(8-(-7))\\\\(y-11)/(x+7)=(-20)/(15)

Now we have to cross multiply:


(y-11)/(x+7)=(-20)/(15)\\\\(y-11).(15)=(x+7).(-20) distributing


15y-165=-20x-140 dividing both sides of the equation in 5


3y-33=-4x-28 adding up 33 in both sides.


3y-33+33=-4x-28+33\\\\3y=-4x+5adding up 4x in both sides of the equation


3y+4x=-4x+5+4x\\\\3y+4x=5

Then the equation that represents the line drawn through (-7,11) and (8,-9) is:

4x+3y=5

And if you resolve the equation
y - 11 = -(4)/(3) (x+7) the result is the same:


y - 11 = -(4)/(3) (x+7)\\\\3(y-11)=-4(x+7)\\\\3y-33=-4x-28\\\\3y+4x=-28+33\\\\4x+3y=5

User German Attanasio
by
7.8k points

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