Answer
After graphing the functions we find that the two intercept at $(2,4)$. The two functions are consistent and independent because they are two different functions that share one intersection point and have different slopes
Work Step by Step
#$1$
The standard notation for linear functions is $y=mx + b$, where m=slope of the function (rise over run) and b=the y-intercept of the function.
#$2$
For Equation 1, $y= 2x$, the $m$ value is $2$, which means the slope is $2$, in other words this means for every increase of 1 in the positive x-direction the y-value will increase by $2$ in the positive y-direction. There is no $b$ value so the y-intercept is $(0,0)$.
$y= 2x; slope=2 and y-intercept= (0,0)$
#$3$
Equation 2, $y= -2+8$, the $m$ value, or slope, is $-2$, which means for every increase of 1 in the positive x-direction the y-value will decrease by 2 There is $b$ value so the y-intercept is (0,8)
$ y= -2x+8; slope= -2 and y-intercept= (0,8)$
#$4$
When we graph the $2$ functions, $Equation 1$ corresponds with $f(x)=2x$ in the $blue color$ and we can see that it has a slope of $2$ and its y-intercept is at $(0,0)$. $Equation 2$ corresponds with $g(x)=8-2x$ in the $red color$ and it has a slope of $-2$ and its y-intercept is at $(0, 8)$. We can see in the graph that the two functions intersect at $(2, 4)$. This means that the two functions equal one another at this point.
#$5$
We can double check our result by making the functions equal one another and solving for x. After doing this we find that the two functions equal one another when $x = 2$. By plugging this back into the functions we can check this again because when $x = 2$ both functions are $y = 4$.
Solution-
$2x = -2x + 8$
$+2x .. +2x$
$4x = 8$
$4x\div4=8\div4$
$x = 2$
