Chapter 4.5, Problem 19P

Multiple Representations Use the table shown at the right.

a. Graph the ordered pairs on a coordinate plane.

b. Write an equation that can be used to find $y$ for any $x$ value.

c. Is the equation a function? Explain.

To determine

To find: We are asked to graph it on coordinate plane.

Answer to Problem 19P

  

Explanation of Solution

Given information: We are given with table of values (1,6), (2,8), (3,10) and (4,12)

Graph:

Let’s represent the points on the xy plane to graph.

  

To determine

To find: We are asked to find the equation for the given values of ‘x’.

Answer to Problem 19P

Rule is $y=2x+4$

Explanation of Solution

Given information: We are given with table of values (1,6), (2,8), (3,10) and (4,12)

Formula: Let’s use $y=mx+b$ . Where ‘ m’ is slope and ‘ b’ is y-intercept.

  $M=\frac{y_2-y_2}{x_2-x_2}$

Calculation:

Let’s use two points from the table to find slope m.

(1,6) and (2,8)

Slope $m=\frac{8-6}{2-1} =2$

Plug in this value into the equation we get $y=2x+b$

Use one of the points to find the value for ‘ b’

Let’s use (1,6)

  $\begin{array}{l}6=2\left(1\right)+b\hfill \\ 6=2+b\hfill \end{array}$

Subtract both sides 2.

b=4

So, equation is y=2x+4

To determine

To find : Does the equation a function?

Answer to Problem 19P

Yes! The equation is a function

Explanation of Solution

Given information: We are given with table of values (1,6), (2,8), (3,10) and (4,12)

Yes! The equation is a function because the linear equations in the form of $y=mx+b$ is a function because it would have unique y value for each x values.