Question

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

Answer 1

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

Answer 2

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+5`adding 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`