Answer:
The ordered pair (6,25) is a solution to both
and ![y=\frac{5}{3}x+15](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B5%7D%7B3%7Dx%2B15)
Step-by-step explanation:
Part 7)
<em>step 1</em>
Find the equation of the line with positive slope
take the points (0,15) and (9,30)
<em>Find the slope</em>
The formula to calculate the slope between two points is equal to
![m=\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
substitute the given values
![m=\frac{30-15}{9-0}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B30-15%7D%7B9-0%7D)
![m=\frac{15}{9}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B15%7D%7B9%7D)
simplify
![m=\frac{5}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B5%7D%7B3%7D)
Find the equation of the line in slope intercept form
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
we have
![m=\frac{5}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B5%7D%7B3%7D)
![b=15](https://tex.z-dn.net/?f=b%3D15)
substitute
![y=\frac{5}{3}x+15](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B5%7D%7B3%7Dx%2B15)
<em>step 2</em>
Find the equation of the line with negative slope
take the points (0,40) and (8,20)
<em>Find the slope</em>
The formula to calculate the slope between two points is equal to
![m=\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
substitute the given values
![m=\frac{20-40}{8-0}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B20-40%7D%7B8-0%7D)
![m=-\frac{20}{8}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B20%7D%7B8%7D)
simplify
![m=-\frac{5}{2}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B5%7D%7B2%7D)
Find the equation of the line in slope intercept form
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
we have
![m=-\frac{5}{2}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B5%7D%7B2%7D)
![b=40](https://tex.z-dn.net/?f=b%3D40)
substitute
![y=-\frac{5}{2}x+40](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B2%7Dx%2B40)
step 3
Find the solution of the system
we know that
The solution of the system of equations is the intersection point both graphs
The intersection point is (6,25) ----> see the graph
therefore
The ordered pair (6,25) is a solution to both
and
![y=\frac{5}{3}x+15](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B5%7D%7B3%7Dx%2B15)