Question

Is the relationship shown by the data linear? If so, model the data with an equation. X:1,5,9,13 Y:5,10,15,20

Answer 1

Let
A (x1,y1)-------> (1,5)
B (x2,y2)------> (5,10)
C (x3,y3)------> (9,15)
D (x4,y4)------> (13,20)

find the slope
AB
m=(10-5)/(5-1)-----> m=5/4

find the slope
CB
m=(15-10)/(9-5)-----> m=5/4

find the slope 
DC
m=(20-15)/(13-9)-----> m=5/4

so
the relationship shown is linear

to model the data with an equation find the equation of a line
with m=5/4 and point A (1,5)
y-y1=m*(x-x1)-----> y-5=(5/4)*(x-1)----> y=1.25x-1.25+5-----> y=1.25x+3.75

the equation to model data is
y=1.25x+3.75

see the attached  figure