Chapter 4, Problem 6CR

To determine

Determine which of the lines ,if any parallel or perpendicular.

Answer to Problem 6CR

Line a and line b is parallel to each other.

Explanation of Solution

Given information:

Line a passes through (0,4) and (4,3).

Line b passes through (0,1) and (4,0).

Line c passes through (2,0) and (4,4).

Calculation:

Formula :

In general slope intercept equation of a line is,

  $y=mx+b$ ….1

where $m$ is the slope of the line and $b$ is the y-intercept.

Finding $m$:

The slope of the line or a linear function is the ration of the change of $y$ over the change in $x$ between any two points on the line .To find the slope of line a passes through (0,4) and (4,3)

  $\begin{array}{c}\text{Slope=change}\text{in}y/\text{change}\text{in}x.\\ m=(y_{2-}{y}_1)/(x_2-x_1).\\ m_a=(3-4)/(4-0).\\ m_a=-1/4.\end{array}$

Slope of line b passes through (0,1) and (4,0).

  $\begin{array}{l}{m}_b=(0-1)/(4-0).\\ m_b=-1/4.\end{array}$

Slope of line c passes through (2,0) and (4,4).

  $\begin{array}{l}{m}_c=(4-0)/(4-2).\\ m_c=1/2.\end{array}$

So, $m_a=m_b\ne m_c.$

Since the slope of line a is equal to the slope of line b so the line a is parallel to line b because all parallel line have same slope .