Chapter 5.3, Problem 36PPE

To determine

To graph:the two lines appear to intersect each other with the help of given information.

Answer to Problem 36PPE

The lines intersect each other.

Explanation of Solution

Given information:

Given table:

X	Y
-2	9
-1	7
0	5
1	3
2	1

X	Y
-2	-18
-1	-14
0	-10
1	-6
2	-2

Calculation:

Consider the table provided for the two lines in the textbook.

Let the slope $m_1$ and $y$ -intercept $c_1$ for first line and the slope $m_2$ and $y$ -intercept $c_2$ for second line. Thus, the two lines are as follows,

  $y=m_{1}x+c_1$

  $y=m_{2}x+c_2$

Now solve to find the values of $m_1,c_1,m_2$ and $c_2$

Use the first table,

Put the points (-2,9) and (-1,7) from first table in $y=m_{1}x+c_1$

Hence,

$9=-2m_1+c_1$

  $7=-m_1+c_1$

After solving the above equations,

  $m_1=-2$ and $c_1=5$

Use the second table,

Put the points $\left(-2,-18\right)\text{ and }\left(-1,-14\right)$ from first table in $y=m_{2}x+c_2$

Hence,

$18=-2m_2+c_2$

  $14=-m_2+c_2$

After solving the above equations,

  $m_2=4$ and $c_2=-10$

Thus, the two equations become as follows,

$y=-2x+5$

  $y=4x-10$

Plot the above lines with the use of table provided in textbook,

From the above figure it is that the lines intersect each other.