Chapter 8.2, Problem 45STP

a.

To determine

To completethe table by filling in the four missing numbers for part A.

Answer to Problem 45STP

  

Explanation of Solution

Given information:Table of values.

  

If we see the $x$ values are increasing by 1 and the corresponding $y$ values are increasing by 2.

So, let’s take the next $x$ value as 4, so, $y$ value is 9+2=11

The last $x$ value is 5, so, $y$ is 11+2 =13.

b.

To determine

To calculate: The rule for the table of values.

Answer to Problem 45STP

Rule is $y=2x+3$ .

Explanation of Solution

Given information: Three table of ordered pairs in the table as (1,5), (2,7) and (3,9).

Formula: Let’s use the $y=mx+b$ , where ‘m’ is slope and ‘b’ is y intercept.

Here the y values are increasing constantly by 2 for each 1 increase of x values.

So, slope m =2

Plug in m as 2 into $y=mx+b$

  $y=2x+b$

Use a point (1,5) for x and y to find value for ‘b’ .

  $5=2(1)+b$

Solve the equation for ‘b’

  $5=2+b$

Subtract both sides 2.

  $3=b$

So, the rule is $y=2x+3$

Conclusion: The rule is $y=2x+3$