Answer:
[tex]y=-\frac{1}{2}x + 1[/tex]
[tex]y=5(\frac{7}{5})^x[/tex]
Step-by-step explanation:
(1)Lets pick two points from the first graph
(0,1) and (2,0)
The graph is linear so we use equation y=mx+b
where m is the slope and b is the y intercept
y intercept at (0,1) so y intercept b = 1
now we find slope m using formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{0-1}{2-0}=\frac{-1}(2}[/tex]
m=-1/2 and b=1 so equation y=mx+b becomes
[tex]y=-\frac{1}{2}x + 1[/tex]
(2) Pick two point from graph (0,5) (1,7)
Since it is an exponential graph, we use y=ab^x
for (0,5) the equation becomes [tex]5=ab^0 so a=5[/tex]
for (1,7) the equation becomes [tex]7=ab^1[/tex]
We know a= 5, so [tex]7=5b^1[/tex]
[tex]b=\frac{7}{5}[/tex]
The equation y=ab^x becomes
[tex]y=5(\frac{7}{5})^x[/tex]
