Answer
The point of intersection is $(4,9)$
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 = \frac{1}{2}x+7$ , the $m$ value is $\frac{1}{2}$, which means the slope is $\frac{1}{2}$ in other words this means for every increase of $2$ in the positive x- direction the y-value will increase by $1$ in the positive y-direction. There is $b$ value of $7$so the y-intercept is $(0,7)$.
$y = \frac{1}{2}x+7;slope= \frac{1}{2} and y−intercept=(0,7)$
#$3$
Equation 2, $y=\frac{3}{2}x+3$, the $m$ value, or slope, is $\frac{3}{2}$, which means for every increase of $2$ in the positive x-direction the y- value will increase by $3$ There is $b$ value so the y-intercept is $(0,3)$
$y=\frac{3}{2}x+3 ;slope=\frac{3}{2} and y−intercept=(0,3)$
#$ 4$
When we graph the $2$ functions, Equation $1$ corresponds with $f(x)=\frac{1}{2}x+7 $ in the $blue color$ and we can see that it has a slope of $\frac{1}{2}$ and its y-intercept is at $(0,7)$.
Equation $2$ corresponds with $g(x)=\frac{3}{2}x+3$ in the $red color$ and it has a slope of $\frac{3}{2}$ and its y-intercept is at $(0,3)$. We can see in the graph that the two functions intersect at $(4,9)$. 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 $x=4$. By plugging this back into the functions we can check this again because when $x=4$ both functions are $y=9$.
Solution-
$\frac{1}{2}x+7 = \frac{3}{2}x+3$
........$-3 . . . . . . .-3$
$ \frac{1}{2}x + 4 = \frac{3}{2}x$
$0.5x + 4 = 1.5x$
$-0.5x . . . . -0.5x$
$4 = 1x$
$x = 4$
