Question

The line represented by the equation 4y + 2x = 33.6 shares a solution point with the line represented by the table

Answer 1

Answer:

The solution of this system is

(4). (6.0,5.4)

Step-by-step explanation:

First we have to find the equation of the line represented in the table; for that we have to find it's slope $m$ and it's y-intercept $b$ and then write it in the following form:

$y=mx+b$

The slope $m$ of the line we get from first two points:

$m=\frac{3.8-3.2}{(-2)-(-5)} =0.2$

thus we have

$y=0.2x+b$

we find $b$ by putting the point $(2,4.6)$ into the function:

$4.6=0.2(2)+b$

$b=4.6-0.4=4.2$

Thus we have

$y=0.2x+4.2$

Now we have to find where this line intersects with $4y+2x=33.6$; to do this we just substitute $y$ with $y=0.2x+4.2$:

$4(0.2x+4.2)+2x=33.6$

$0.8x+16.8+2x=33.6$

$\boxed{x=6 }$

We have the x-coordinate of  the intersection.

We find the y-coordinate by substituting $x=6$ into $y=0.2x+4.2$:

$y=0.2(6)+4.2=5.4$

$\boxed{y=5.4}$

Thus the solution to the system is

$\boxed{(x,y)=(6, 5.4)}$

which is option 4.