Solution:
The Ordered pair of the function is
x : 0 1 2 3 4 5
y: 13 21 29 37 45 53
(a) [tex]\frac{\text{Change in y values}}{\text{Change in x values}}=\frac{21-13}{1-0}=\frac{29-21}{2-1}=\frac{37-29}{3-2}=\frac{45-37}{4-3}=\frac{53-45}{5-4}=8[/tex]
Slope between two points are same.So,the function Represented in terms of ordered pairs Linear.
(b) As, you can each Successor of x values is obtained by adding 1 to it's Predecessor.
and , each Successor of y values is obtained by adding 8 to it's Predecessor.
(c) Taking any two ordered pairs , (0,13) and (1,21) we can find an equation of line passing through these 5 points (2,29),(3,37),(4,45),(5,53)
Equation of line passing through passing through two points [tex](x_{1},y_{1}),{\text and} (x_{2},y_{2})[/tex] is given by
= [tex]\frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
= [tex]\frac{y-13}{x-0}=\frac{21-13}{1-0}[/tex]
→ y -13 = 8 x
→ y = 8 x + 13
So, Y intercept = 13
