Answer:
[tex]y=19.7*10^{3}[/tex]
Step-by-step explanation:
step 1
Find the slope
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex](-200,-4.03*10^{4}), (50,9.7*10^{3})[/tex]
convert to
[tex](-200,-40.3*10^{3}), (50,9.7*10^{3})[/tex]
substitute in the formula
[tex]m=\frac{9.7*10^{3}+40.3*10^{3}}{50+200}[/tex]
[tex]m=\frac{50*10^{3}}{250}[/tex]
[tex]m=200[/tex]
step 2
Find the equation of the line into point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex](x1,y1)=(50,9.7*10^{3})[/tex]
[tex]m=200[/tex]
substitute
[tex]y-9.7*10^{3}=200(x-50)[/tex] ----> equation of the line into point slope form
step 3
Find the value of y when x=100
substitute in the equation the value of x
[tex]y-9.7*10^{3}=200(100-50)[/tex]
[tex]y=200(50)+9.7*10^{3}[/tex]
[tex]y=19,700[/tex]
[tex]y=19.7*10^{3}[/tex]
