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

Answer:

4x + 3y = 5

Step-by-step explanation:

Given

y - 11 = - $\frac{4}{3}$(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

Answer:

4x+3y=5

Step-by-step explanation:

We have the equation $y-11=-\frac{4}{3} (x+7)$ 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:

$\frac{y-y_{1}}{x-x_{1}} =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$,

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:

$\frac{y-y_{1}}{x-x_{1}} =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\frac{y-11}{x-(-7)}=\frac{(-9)-11}{8-(-7)}$

Now we have to resolve the equation:

$\frac{y-11}{x-(-7)}=\frac{(-9)-11}{8-(-7)}\\\\\frac{y-11}{x+7}=\frac{-20}{15}$

Now we have to cross multiply:

$\frac{y-11}{x+7}=\frac{-20}{15}\\\\(y-11).(15)=(x+7).(-20)$ 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 $y - 11 = -\frac{4}{3} (x+7)$ the result is the same:

$y - 11 = -\frac{4}{3} (x+7)\\\\3(y-11)=-4(x+7)\\\\3y-33=-4x-28\\\\3y+4x=-28+33\\\\4x+3y=5$