Answer:
4x + 3y = 5
Step-by-step explanation:
Given
y - 11 = - [tex]\frac{4}{3}[/tex](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:
4x+3y=5
Step-by-step explanation:
We have the equation [tex]y-11=-\frac{4}{3} (x+7)[/tex] 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:
[tex]\frac{y-y_{1}}{x-x_{1}} =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex],
and the points are [tex](x_{1},y_{1}) , (x_{2},y_{2})[/tex]
In this case:
[tex](x_{1},y_{1})=(-7,11)\\(x_{2},y_{2})=(8,-9)[/tex]
Replacing the points in the equation:
[tex]\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)}\\[/tex]
Now we have to resolve the equation:
[tex]\frac{y-11}{x-(-7)}=\frac{(-9)-11}{8-(-7)}\\\\\frac{y-11}{x+7}=\frac{-20}{15}[/tex]
Now we have to cross multiply:
[tex]\frac{y-11}{x+7}=\frac{-20}{15}\\\\(y-11).(15)=(x+7).(-20)[/tex] distributing
[tex]15y-165=-20x-140[/tex] dividing both sides of the equation in 5
[tex]3y-33=-4x-28[/tex] adding up 33 in both sides.
[tex]3y-33+33=-4x-28+33\\\\3y=-4x+5 [/tex]adding up 4x in both sides of the equation
[tex]3y+4x=-4x+5+4x\\\\3y+4x=5[/tex]
Then the equation that represents the line drawn through (-7,11) and (8,-9) is:
4x+3y=5
And if you resolve the equation [tex]y - 11 = -\frac{4}{3} (x+7)[/tex] the result is the same:
[tex]y - 11 = -\frac{4}{3} (x+7)\\\\3(y-11)=-4(x+7)\\\\3y-33=-4x-28\\\\3y+4x=-28+33\\\\4x+3y=5[/tex]
