Answer:
Ques 4)
The system is:
[tex]y=x-4[/tex]
[tex]y=\dfrac{x-4}{x+2}[/tex]
Ques 5)
The system is:
[tex]6x+y=-27[/tex]
and [tex]y=x^2+5x+3[/tex]
Step-by-step explanation:
Ques 4)
After looking at the graph we observe that :
The first graph is a line which passes through (4,0) and (0,-4)
Hence, the equation of such a line is:
y=x-4
and the second graph is a curve such that the vertical asymptote is at x= -2
and also x= 4 is a root of the rational function.
Since, the graph passes through (4,0)
Hence, the system equation which best represents the graph is:
[tex]y=x-4[/tex]
[tex]y=\dfrac{x-4}{x+2}[/tex]
Ques 5)
One of the curve is :
a line that passes through (-5,3) and (-6,9)
Hence, the equation of line is given by:
[tex]y-3=\dfrac{9-3}{-6-(-5)}\times (x-(-5))\\\\i.e.\\\\y-3=\dfrac{6}{-6+5}\times (x+5)\\\\i.e.\\\\y-3=\dfrac{6}{-1}\times (x+5)\\\\i.e.\\\\y-3=-6(x+5)\\\\i.e.\\\\y-3=-6x-30\\\\i.e.\\\\y=-6x-30+3\\\\i.e.\\\\y=-6x-27[/tex]
i.e. Equation of line is:
[tex]6x+y=-27[/tex]
While the other graph is a upward facing parabola such that the vertex is in third quadrant this means that the coefficient of x^2 must be positive and that of x must also be positive.
Hence, the system in which the equation of line satisfies is:
[tex]6x+y=-27[/tex]
and [tex]y=x^2+5x+3[/tex]
