Answer:
[tex]y=\frac{3}{4}-1[/tex] and [tex]y=-\frac{4}{3}+9[/tex]
Step-by-step explanation:
step 1
Find the equation of the blue line
take the points
(0,-1) and (8,5) from the graph
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{5+1}{8-0}[/tex]
[tex]m=\frac{6}{8}[/tex]
simplify
[tex]m=\frac{3}{4}[/tex]
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=\frac{3}{4}[/tex]
[tex]b=-1[/tex] ---> see the graph
substitute the given values
[tex]y=\frac{3}{4}-1[/tex]
step 2
Find the equation of the black line
take the points
(0,9) and (3,5) from the graph
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{5-9}{3-0}[/tex]
[tex]m=-\frac{4}{3}[/tex]
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=-\frac{4}{3}[/tex]
[tex]b=9[/tex] ---> see the graph
substitute the given values
[tex]y=-\frac{4}{3}+9[/tex]
therefore
The system of equations is
[tex]y=\frac{3}{4}-1[/tex] and [tex]y=-\frac{4}{3}+9[/tex]
