Answer:
The ordered pair (6,25) is a solution to both
[tex]y=-\frac{5}{2}x+40[/tex] and [tex]y=\frac{5}{3}x+15[/tex]
Step-by-step explanation:
Part 7)
step 1
Find the equation of the line with positive slope
take the points (0,15) and (9,30)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the given values
[tex]m=\frac{30-15}{9-0}[/tex]
[tex]m=\frac{15}{9}[/tex]
simplify
[tex]m=\frac{5}{3}[/tex]
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=\frac{5}{3}[/tex]
[tex]b=15[/tex]
substitute
[tex]y=\frac{5}{3}x+15[/tex]
step 2
Find the equation of the line with negative slope
take the points (0,40) and (8,20)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the given values
[tex]m=\frac{20-40}{8-0}[/tex]
[tex]m=-\frac{20}{8}[/tex]
simplify
[tex]m=-\frac{5}{2}[/tex]
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=-\frac{5}{2}[/tex]
[tex]b=40[/tex]
substitute
[tex]y=-\frac{5}{2}x+40[/tex]
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 [tex]y=-\frac{5}{2}x+40[/tex] and
[tex]y=\frac{5}{3}x+15[/tex]
